[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/14529#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/14529","headline":"\u30d1\u30fc\u30d5\u30a7\u30af\u30c8\u30ca\u30f3\u30d0\u30fc – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2","name":"\u30d1\u30fc\u30d5\u30a7\u30af\u30c8\u30ca\u30f3\u30d0\u30fc – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2","description":"before-content-x4 \u81ea\u7136\u6570 n {displaystyle n} after-content-x4 \u306a\u308a\u307e\u3059 \u5b8c\u74a7\u306a\u6570 \uff08\u307e\u305f \u5b8c\u74a7\u306a\u6570 \uff09\u5408\u8a08\u306e\u5408\u8a08\u3068\u547c\u3070\u308c\u307e\u3059 a \u2217 \uff08 n \uff09\uff09 {displaystyle sigma ^{*}\uff08n\uff09} \u305d\u308c\u81ea\u4f53\u3092\u9664\u304f\u3059\u3079\u3066\u306e\uff08\u30dd\u30b8\u30c6\u30a3\u30d6\u306a\uff09\u9664\u6570\u3067\u3059\u3002\u540c\u7b49\u306e\u5b9a\u7fa9\u306f\u3001\u5b8c\u74a7\u306a\u6570\u5b57\u3067\u3059","datePublished":"2019-05-09","dateModified":"2019-05-09","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/a601995d55609f2d9f5e233e36fbe9ea26011b3b","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/a601995d55609f2d9f5e233e36fbe9ea26011b3b","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/14529","wordCount":16881,"articleBody":" (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4\u81ea\u7136\u6570 n {displaystyle n} (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u306a\u308a\u307e\u3059 \u5b8c\u74a7\u306a\u6570 \uff08\u307e\u305f \u5b8c\u74a7\u306a\u6570 \uff09\u5408\u8a08\u306e\u5408\u8a08\u3068\u547c\u3070\u308c\u307e\u3059 a \u2217 \uff08 n \uff09\uff09 {displaystyle sigma ^{*}\uff08n\uff09} \u305d\u308c\u81ea\u4f53\u3092\u9664\u304f\u3059\u3079\u3066\u306e\uff08\u30dd\u30b8\u30c6\u30a3\u30d6\u306a\uff09\u9664\u6570\u3067\u3059\u3002\u540c\u7b49\u306e\u5b9a\u7fa9\u306f\u3001\u5b8c\u74a7\u306a\u6570\u5b57\u3067\u3059 n {displaystyle n} \u306f\u3001\u3059\u3079\u3066\u306e\u80af\u5b9a\u7684\u306a\u9664\u6570\uff08\u305d\u308c\u81ea\u4f53\u3092\u56f2\u3093\u3067\u3044\u308b\uff09\u306e\u5408\u8a08\u306e\u534a\u5206\u306e\u5927\u304d\u3055\u306e\u6570\u5b57\u3067\u3059\u3002 H. (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4a \uff08 n \uff09\uff09 = 2 n {displaystyle sigma\uff08n\uff09= 2n} \u3002\u6700\u5c0f\u306e3\u3064\u306e\u5b8c\u5168\u306a\u6570\u5b57\u306f6\u300128\u3001496\u3067\u3059\u3002\u4f8b\uff1a28\u306e\u6b63\u306e\u9664\u6570\u306f1\u30012\u30014\u30017\u300114\u300128\u3067\u3042\u308a\u3001\u6b21\u306e\u3082\u306e\u304c\u9069\u7528\u3055\u308c\u307e\u3059 \u521d\u3081 + 2 + 4 + 7 + 14 = 28\u3002 {displaystyle 1+2+4+7+14 = 28.} \u3059\u3079\u3066\u306e\u65e2\u77e5\u306e\u5b8c\u5168\u306a\u6570\u5b57\u306f\u307e\u3063\u3059\u3050\u3067\u3001Mersenne Prim Numbers\u304b\u3089\u6d3e\u751f\u3057\u3066\u3044\u307e\u3059\u3002\u5947\u5999\u306a\u5b8c\u74a7\u306a\u6570\u5b57\u304c\u3042\u308b\u304b\u3069\u3046\u304b\u306f\u4e0d\u660e\u3067\u3059\u3002\u30ae\u30ea\u30b7\u30e3\u306e\u53e4\u4ee3\u3067\u3055\u3048\u3001\u5b8c\u5168\u306a\u6570\u5b57\u304c\u77e5\u3089\u308c\u3066\u3044\u305f\u305f\u3081\u3001\u305d\u308c\u3089\u306e\u6700\u3082\u91cd\u8981\u306a\u7279\u6027\u306f\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u8981\u7d20\u3067\u6271\u308f\u308c\u307e\u3057\u305f\u3002 6\u307e\u305f\u306f8\u3067\u7d42\u308f\u308b\u3059\u3079\u3066\u306e\u30b9\u30c8\u30ec\u30fc\u30c8\u306a\u5b8c\u5168\u306a\u6570\u5b57\u306f\u3001\u591a\u304f\u306e\u5834\u5408\u3001\u5f37\u5927\u3067\u6570\u79d8\u8853\u7684\u306a\u89e3\u91c8\u306e\u5bfe\u8c61\u306e\u5bfe\u8c61\u3067\u3057\u305f\u3002 \u682a\u5f0f\u91d1\u984d a \u2217 \uff08 j \uff09\uff09 {displaystyle sigma ^{*}\uff08j\uff09} \u6570 (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4j {displaystyle j} \u5fc5\u7136\u7684\u306b\u5c0f\u3055\u3044\u3001\u3088\u308a\u5927\u304d\u3044\u304b\u7b49\u3057\u3044 j {displaystyle j} \u3002\u6700\u521d\u306e\u30b1\u30fc\u30b9\u3067\u306f j {displaystyle j} 2\u756a\u76ee\u306e\u30b1\u30fc\u30b9\u3067\u306f\u8c4a\u5bcc\u3067\u30013\u756a\u76ee\u306e\u30b1\u30fc\u30b9\u3067\u306f\u5b8c\u5168\u306b\u4e0d\u8db3\u3057\u3066\u3044\u307e\u3059\u3002\u4e0d\u5341\u5206\u3067\u8c4a\u5bcc\u306a\u6570\u5b57\u3068\u306f\u5bfe\u7167\u7684\u306b\u3001\u5b8c\u5168\u306a\u6570\u5b57\u306f\u975e\u5e38\u306b\u307e\u308c\u3067\u3059\u3002\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u306f\u3059\u3067\u306b\u3001\u3053\u306e\u7528\u8a9e\u306e\u6700\u521d\u306e4\u3064\u306e\u5b8c\u5168\u306a\u6570\u5b57\u304c 2 k\u22121\uff08 2 k – \u521d\u3081 \uff09\uff09 {displaystyle 2^{k-1}\uff082^{k} -1\uff09} \u306e\u8a3c\u660e\u306b\u3088\u3063\u3066 k {displaystyle k} \u9069\u5207\u306a\u6570\u5b57\u3067\uff1a \u6700\u521d\u306e12\u500b\u306e\u5b8c\u5168\u306a\u6570\u5b57\u306f\uff08\u7d50\u679c\u3067\u3059 A000396 OEIS\u3067\uff09\uff1a 6 28 496 8.128 33,550.336 8.589.869.056 137.438.691.328 2.305.843.008.139.952.128 2.658.455.991.569.831.744.654.\u200b\u200b692.615.953.842.1766 191.561.942.608.236.107.294.793.378.084.303.638.130.997.321.548.169.216 13.164.036.458.569.648.337.239.753.460.458.722.910.223.472.318.386.943.117.783.78.1288888888888888888888888888888888888888888888888888888888888888888888888 14.474.011.154.664.524.427.946.373.126.085.988.481.573.677.491.474.835.889.066.354.349.131.199.152.12888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888\u5e74\u533a\u300d 888888888888888888888888888888888888888888888 \u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u306f\u305d\u308c\u3092\u8a3c\u660e\u3057\u307e\u3057\u305f 2 k – \u521d\u3081 \uff08 2 k – \u521d\u3081 \uff09\uff09 {displaystyle 2^{k-1}\uff082^{k} -1\uff09} \u5e38\u306b\u5b8c\u74a7\u306a\u6570\u5b57\u306f\u3044\u3064\u3067\u3059\u304b m k = 2 k – \u521d\u3081 {displaystyle m_ {k} = 2^{k} -1} \u4e3b\u8981\u306a\u6570\u5b57\u3067\u3059\u3002\u3053\u308c\u3089\u306f\u3044\u308f\u3086\u308bMersenne\u30d7\u30ea\u30e0\u756a\u53f7\u3067\u3059\u3002\u307b\u307c2000\u5e74\u5f8c\u3001Leonhard Euler\u306f\u3001\u3053\u306e\u3088\u3046\u306b\u3057\u3066\u3059\u3079\u3066\u306e\u30b9\u30c8\u30ec\u30fc\u30c8\u6570\u3092\u4f5c\u6210\u3067\u304d\u308b\u3053\u3068\u3092\u8a3c\u660e\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002 \u7279\u306b\u5b8c\u5168\u306a\u6570\u5b57\u3068Mersenne\u306e\u30d7\u30ea\u30e0\u756a\u53f7\u304c\u660e\u78ba\u306b\u4e92\u3044\u306b\u5272\u308a\u5f53\u3066\u3089\u308c\u3066\u3044\u307e\u3059\u3002 2019\u5e741\u6708\u307e\u3067\u306b\u300151\u4eba\u306e\u30e1\u30eb\u30bb\u30f3\u30d7\u30ea\u30e0\u304c\u77e5\u3089\u308c\u3066\u3044\u307e\u3057\u305f\u3002\u305d\u3057\u3066\u3001\u6b21\u306e\u9ad8\u3044\u6570\u306e\u305f\u3081\u306b k {displaystyle k} \uff1a2\u30013\u30015\u30017\u300113\u300117\u300119\u300131\u300161\u300189\u3001107\u3001127\u3001521\u3001607\u30011,279\u30012,203\u30012,281\u30013,217\u30014.253\u30014.423\u30019.689\u30019.941\u300111.213\u30011937\u300121.701\u300133,209\u300144.497\u300121.701\u300133,209\u300144.497 1325\u30018043\u300170739 .787\u30011,398.269\u30012,976.221\u30013,021,377\u30016,972,593\u300113,466,917\u300120.996.011\u300124,036,583\u300125.964.951\u300130.402.572.572.572.572.572.572.572.5457 6.667\u300142.643.801\u300143.112.609\u300157.885.161 89,933\u3002 [\u521d\u3081] \uff08\u7d50\u679c A000043 OEIS\u3067\uff09 \u7121\u9650\u306e\u6570\u306e\u5b8c\u74a7\u306a\u6570\u5b57\u304c\u3042\u308b\u304b\u3069\u3046\u304b\u306f\u30aa\u30fc\u30d7\u30f3\u3067\u3059\u3002 \u7121\u9650\u306e\u6570\u306e\u5b8c\u74a7\u306a\u6570\u5b57\u304c\u3042\u308b\u304b\u3069\u3046\u304b\u306f\u30aa\u30fc\u30d7\u30f3\u3067\u3059\u3002\u3053\u306e\u8cea\u554f\u306f\u3001Mersenne\u30d7\u30ea\u30e0\u756a\u53f7\u306e\u7121\u9650\u306e\u6570\u304c\u3042\u308b\u304b\u3069\u3046\u304b\u306e\u554f\u984c\u3068\u4e00\u81f4\u3057\u3066\u3044\u307e\u3059\u3002 \u5947\u5999\u306a\u30d5\u30eb\u756a\u53f7\u304c\u3042\u308b\u304b\u3069\u3046\u304b\u306f\u30aa\u30fc\u30d7\u30f3\u3067\u3059\u3002\u305d\u306e\u3088\u3046\u306a\u6570\u304c\u5b58\u5728\u3059\u308b\u5834\u5408\u3001\u6b21\u306e\u7279\u6027\u304c\u3042\u308a\u307e\u3059\u3002 [2] [3] [4] Table of Contents\u76f8\u4e92\u9664\u6570\u306e\u5408\u8a08 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u30a4\u30fc\u30c8\u30f3\u306e\u8868\u73fe\uff081995\u30011996\uff09 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u6700\u521d\u306e\u5947\u5999\u306a\u81ea\u7136\u6570\u306e\u7acb\u65b9\u4f53\u306e\u5408\u8a08 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u6700\u521d\u306e\u81ea\u7136\u6570\u306e\u5408\u8a08 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u5225\u306e\u8868\u73fe [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u30d0\u30a4\u30ca\u30ea\u30fc\u30b7\u30b9\u30c6\u30e0 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u7b2c\u56db\u7d00\u30b7\u30b9\u30c6\u30e0 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u8c4a\u5bcc\u3067\u4e0d\u5341\u5206\u306a\u6570 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u53cb\u9054\u306e\u53cb\u9054\u3068\u5384\u4ecb\u306a\u6570\u5b57 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u64ec\u4f3c\u30d5\u30a3\u30ae\u30e5\u30a2 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u5947\u5999\u306a\u6570\u5b57\u3084\u5947\u5999\u306a\u6570\u5b57 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] seried\u756a\u53f7 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u6e96\u7570\u306a\u308b\u6570\u5b57 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] SuperPerfects\u3092\u652f\u6255\u3044\u307e\u3059 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u30dc\u30a8\u30c6\u30a3\u30a6\u30b9 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u30d0\u30a4\u30d6\u30ec\u30ad\u30bb\u30fc\u30bc [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u8a69 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u76f8\u4e92\u9664\u6570\u306e\u5408\u8a08 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u5b8c\u5168\u306a\u6570\u306e\u3059\u3079\u3066\u306e\u90e8\u5206\u306e\u76f8\u4e92\u5024\u306e\u5408\u8a08 n {displaystyle n} \uff08\u756a\u53f7\u81ea\u4f53\u3092\u542b\u3080\uff09\u306f2\u306b\u306a\u308a\u307e\u3059\u3002 \u2211 k\u2223n1k= \u2211 k\u2223nkn= 1na \uff08 n \uff09\uff09 = 2nn= 2 {displaystyle sum _ {kmid n} {frac {1} {k}} = sum _ {kmid n} {k} {n}} = {frac {1} {n}} sigma\uff08n\uff09= {frac {n} {n} = 2} \u4f8b\uff1a \u305f\u3081\u306b n = 6 {displaystyle n = 6} \u8a72\u5f53\u3059\u308b\uff1a 11+ 12+ 13+ 16= 126= 2 {displaystyle {frac {1} {1}}+{frac {1} {2}}+{frac {1} {3}}+{frac {1} {6}} = {frac {12} {6}}} = 2} = 2} \u30a4\u30fc\u30c8\u30f3\u306e\u8868\u73fe\uff081995\u30011996\uff09 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u3059\u3079\u3066\u306e\u5b8c\u74a7\u306a\u756a\u53f7n> 6\u306b\u30d7\u30ec\u30bc\u30f3\u30c6\u30fc\u30b7\u30e7\u30f3\u304c\u3042\u308a\u307e\u3059 n = \u521d\u3081 + 92k \uff08 k + \u521d\u3081 \uff09\uff09 {displaystyle n = 1+{frac {9} {2}} k\uff08k+1\uff09} \u3068 k = 8 j + 2 {displaystyle k = 8j+2} \u304a\u3088\u3073\u975e\u9670\u6027\u306e\u6570 j {displaystyle j} \u3002 \u9006\u306b\u3001\u3042\u306a\u305f\u306f\u81ea\u7136\u6570\u3092\u53d6\u5f97\u3057\u307e\u305b\u3093 j {displaystyle j} \u5b8c\u74a7\u306a\u6570\u3002 \u4f8b\uff1a j = 0 {displaystyle j = 0} \u7d50\u679c k = 2 {displaystyle k = 2} \u3068 n = 28 {displaystyle n = 28} \uff08\u5b8c\u5168\u306b\uff09\u3002 j = \u521d\u3081 {displaystyle j = 1} \u7d50\u679c k = \u5341 {displaystyle k = 10} \u3068 n = 496 {displaystyle n = 496} \uff08\u5b8c\u5168\u306b\uff09\u3002 j = 2 {displaystyle j = 2} \u7d50\u679c k = 18 {displaystyle k = 18} \u3068 n = 1540 {displaystyle n = 1540} \uff08\u5b8c\u5168\u3067\u306f\u3042\u308a\u307e\u305b\u3093\uff09\u3002 \u6700\u521d\u306e\u5947\u5999\u306a\u81ea\u7136\u6570\u306e\u7acb\u65b9\u4f53\u306e\u5408\u8a08 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] 6\u3092\u9664\u3044\u3066\u3001\u3059\u3079\u3066\u306e\u5b8c\u74a7\u306a\u6570\u5b57\u306f n {displaystyle n} \u8868\u793a n = \u2211 k=12p\u221212 \uff08 2 k – \u521d\u3081 \uff09\uff09 3\u3001 {displaystyle n = sum _ {k = 1}^{2^{frac {p-1} {2}}}\u301c\uff082k-1\uff09^{3}\u3001} \u3057\u305f\u304c\u3063\u3066 p {displaystyle p} \u30d7\u30ec\u30bc\u30f3\u30c6\u30fc\u30b7\u30e7\u30f3\u304b\u3089\u306eMersenne Prim\u306e\u6307\u6570 n = 2 p – \u521d\u3081 \uff08 2 p – \u521d\u3081 \uff09\uff09 {displaystyle n = 2^{p-1}\uff082^{p} -1\uff09} \u306f\u3002 \u4f8b\uff1a 28 = \u521d\u3081 3+ 3 3{displaystyle 28 = 1^{3}+3^{3}} 496 = \u521d\u3081 3+ 3 3+ 5 3+ 7 3{displaystyle 496 = 1^{3}+3^{3}+5^{3}+7^{3}} \u8ff0\u3079\u308b\uff1a \u305d\u308c\u305e\u308c\u306e\u305f\u3081 m \u2208 n {displaystyle min mathbb {n}} \u3068 Q = m 2 {displaystyle q = m^{2}} \u8a72\u5f53\u3059\u308b\uff1a \u2211 k=1m\uff08 2 k – \u521d\u3081 \uff09\uff09 3= 2 m 4 – m 2= Q de \uff08 2 Q – \u521d\u3081 \uff09\uff09 {displaystyle sum _ {k = 1}^{m}\uff082k-1\uff09^{3} = 2m^{4} -m^{2} = qcdot\uff082q-1\uff09} \uff08\u4e0d\u30d1\u30c3\u30c8\u30ad\u30e5\u30fc\u30d3\u30c3\u30af\u6570\u306e\u5f0f\u306e\u5408\u8a08\uff09\u3002 \u7279\u306b\u3001\u3053\u308c\u306f2\u3064\u306e\u5f37\u5ea6\u3059\u3079\u3066\u306b\u3082\u9069\u7528\u3055\u308c\u307e\u3059 m = 2 r {displaystyle m = 2^{r}} \u3068 Q = \uff08 2 2 \uff09\uff09 r {displaystyle q =\uff082^{2}\uff09^{r}} \u3068 r \u2208 n {displaystyle rin mathbb {n}} \u306b\uff1a \u2211 k=12r\uff08 2 k – \u521d\u3081 \uff09\uff09 3= 2 \uff08 2 r\uff09\uff09 4 – \uff08 2 r\uff09\uff09 2= \uff08 2 2\uff09\uff09 r\uff08 2 de \uff08 2 2\uff09\uff09 r – \u521d\u3081 \uff09\uff09 {displaystyle sum _ {k = 1}^{2^{r}}\uff082k-1\uff09^{3} = 2\u3001\uff082^{r}\uff09^{4} – \uff082^{r}\uff09^{2} =\uff082^{2}\uff09^{r}\u3001\uff082cdot\uff082^{2}\uff09 \u4e8b\u6545\u3067 p {displaystyle p} \u3042\u306a\u305f\u306f\u3067\u304d\u308b r = p\u221212 {displaystyle r = {frac {p-1} {2}}} \u4ee3\u308f\u308a\u306e\uff1a \u2211 k=12p\u221212\uff08 2 k – \u521d\u3081 \uff09\uff09 3= 2 \uff08 2 p\u221212\uff09\uff09 4 – \uff08 2 p\u221212\uff09\uff09 2= \uff08 2 2\uff09\uff09 p\u221212\uff08 2 de \uff08 2 2\uff09\uff09 p\u221212 – \u521d\u3081 \uff09\uff09 = 2 p\u22121\uff08 2 de 2 p\u22121 – \u521d\u3081 \uff09\uff09 {displaystyle sum _ {k = 1}^{2^{frac {p-1} {2}}}}\uff082k-1\uff09^{3} = 2\u3001\uff082^{frac {p-1} {2}}\uff09^{4} – \uff082^{frac {2} {2} {2}^{2} {2} {2} {2^{} {2^} ac {p-1} {2}}\u3001\uff082cdot\uff082^{2}\uff09^{frac {p-1} {2}} – 1\uff09= 2^{p-1}\u3001\uff082cdot 2^{p-1} -1\uff09} \u2211 k=12p\u221212\uff08 2 k – \u521d\u3081 \uff09\uff09 3= 2 p\u22121\uff08 2 p – \u521d\u3081 \uff09\uff09 {displaystyle sum _ {k = 1}^{2^{frac {p-1} {2}}}\uff082k-1\uff09^{3} = 2^{p-1}\u3001\uff082^{p} -1\uff09} \u7acb\u65b9\u4f53\u306e\u5408\u8a08\u3068\u3057\u3066\u306e\u30d7\u30ec\u30bc\u30f3\u30c6\u30fc\u30b7\u30e7\u30f3\u306f\u3001\u5b8c\u74a7\u306a\u6570\u5b57\u3092\u6301\u3064\u975e\u5e38\u306b\u9593\u63a5\u7684\u306b\u4f55\u304b\u306e\u307f\u3067\u3042\u308b\u30d7\u30ed\u30d1\u30c6\u30a3\u3067\u3059 n = 2 p\u22121\uff08 2 p – \u521d\u3081 \uff09\uff09 = 6 \u3001 28 \u3001 496 \u3001 8128 \u3001 33550336 \u3001 … {displaystyle n = 2^{p-1}\uff082^{p} -1\uff09= 6,496,8128,33550336\u3001dotsc} p = 2\u30013\u30014\u30015\u30016\u3067… \u3057\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\uff08\u6700\u521d\u306e\u5b8c\u5168\u306a\u6570\u5024n\uff08p = 2\uff09= 6\u3092\u524a\u9664\u3057\u3001\u73cd\u3057\u3044\u30d5\u30eb\u756a\u53f7\u304c\u306a\u3044\u3068\u4eee\u5b9a\u3057\u3066\uff09\u304c\u3001\u6570\u5b57\u30b7\u30ea\u30fc\u30ba\u306e\u30d7\u30ed\u30d1\u30c6\u30a3 n \u2217= 2 m 4 – m 2= 0 \u3001 \u521d\u3081 \u3001 28 \u3001 153 \u3001 496 \u3001 1225 \u3001 2556 \u3001 4753 \u3001 8128 \u3001 13041 \u3001 … {displaystyle n^{*} = 2m^{4} -m^{2} = 0,1,28,153,496,1225,2556,4753,8128,13041\u3001dotsc} \u306f\u3002\u307e\u305f\u3001\u5f7c\u5973\u304c\u6700\u521d\u306e\u5b8c\u5168\u306a\u6570\u5b57\u306b\u9069\u7528\u3067\u304d\u306a\u3044\u7406\u7531\u3082\u308f\u304b\u308a\u307e\u3059\uff08 p = 2 {displaystyle p = 2} \u3057\u305f\u304c\u3063\u3066\u3001\u5947\u5999\u3067\u306f\u3042\u308a\u307e\u305b\u3093 r {displaystyle r} \u6574\u6570\u3067\u306f\u3042\u308a\u307e\u305b\u3093\uff09\u3002 \u3061\u306a\u307f\u306b\u3001\u3053\u306e\u65b9\u7a0b\u5f0f\u306f\u6570\u5b57\u306e\u3082\u306e\u3067\u3059 n \u2217 < \u5341 50 {displaystyle n^{*} i=1k\u79c1 = k(k+1)2{displaystyle n = 1+2+3+dots+k = sum _ {i = 1}^{k} i = {frac {k\uff08k+1\uff09} {2}}}} \u3057\u305f\u304c\u3063\u3066 k {displaystyle k} \u30b9\u30da\u30eb\u3068\u540c\u3058\u6570 2 k – \u521d\u3081 \uff08 2 k – \u521d\u3081 \uff09\uff09 {displaystyle 2^{k-1}\uff082^{k} -1\uff09} \u306f\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u5b8c\u74a7\u306a\u5404\u6570\u306f\u3001\u4e09\u89d2\u5f62\u306e\u6570\u5b57\u3067\u3082\u3042\u308a\u307e\u3059\u3002 \u4f8b\uff1a 6 = \u521d\u3081 + 2 + 3 = 3\u22c542{displaystyle 6 = 1+2+3 = {frac {3cdot 4} {2}}}} 28 = \u521d\u3081 + 2 + 3 + 4 + 5 + 6 + 7 = 7\u22c582{displaystyle 28 = 1+2+3+4+5+6+7 = {frac {7cdot 8} {2}}} 496 = \u521d\u3081 + 2 + 3 + 4 + 5 + \u22ef + \u6700\u521d\u306b30 = 31\u22c5322{displaystyle 496 = 1+2+3+4+5+dotsb+31 = {frac {31cdot 32} {2}}} 8128 = \u521d\u3081 + 2 + 3 + 4 + 5 + \u22ef + 127 = 127\u22c51282{displaystyle 8128 = 1+2+3+4+5+dotsb+127 = {frac {127cdot 128} {2}}} \u5225\u306e\u8868\u73fe [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u3059\u3079\u3066\u306e\u5b8c\u74a7\u306a\u6570 n {displaystyle n} \u9069\u5207\u306a\u81ea\u7136\u6570\u3092\u6301\u3064\u3053\u3068\u304c\u3067\u304d\u307e\u3059 k {displaystyle k} \u8868\u793a n = (2k2)\u3002 {displaystyle n = {binu {2^{k} {{}}\u3002}\u3002}\u3002 \u30d0\u30a4\u30ca\u30ea\u30fc\u30b7\u30b9\u30c6\u30e0 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u30c7\u30e5\u30a2\u30eb\u30b7\u30b9\u30c6\u30e0\u306b\u306f\u30011\u3064\u3068\u30bc\u30ed\u306e\u7279\u5fb4\u7684\u306a\u7d50\u679c\u3068\u3057\u3066\u3001\u5b8c\u5168\u306a\u6570\u5b57\u304c\u8868\u793a\u3055\u308c\u307e\u3059\u3002 \u305d\u306e\u5f62\u306e\u305f\u3081 \uff08 2p+1 – \u521d\u3081 \uff09\uff09 de 2 p {displaystyle\u5de6\uff082^{p+1} -1 right\uff09cdot 2^{p}} \u306e\u7d50\u679c\u3068\u3057\u3066\u3001\u6570\u5024\u30b7\u30b9\u30c6\u30e0\u306e2\u756a\u76ee\u306b\u7acb\u3063\u3066\u3044\u307e\u3059 p + \u521d\u3081 {displaystyle p+1} \u733f\u3068 p {displaystyle p} \u30bc\u30ed\u30b9\u30c0\u30fc\u30eb\uff1a 6 = 110 2{displaystyle 6 = 110_ {2}} 28 = 11100 2{displaystyle 28 = 11100_ {2}} 496 = 111110000 2{displaystyle 496 = 111110000_ {2}} 8128 = 1111111000000 2{displaystyle 8128 = 1111111000000_ {2}} 33550336 = 11111111111111110000000000 2{displaystyle 33550336 = 111111111111110000000000_ {2}}} \u7b2c\u56db\u7d00\u30b7\u30b9\u30c6\u30e0 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u3061\u3087\u3046\u3069\u5b8c\u74a7\u306a\u6570 6″>\u56db\u6b21\u7cfb\u306b\u306f\u30013\u3064\u306e\u30bc\u30ed\u306e\u7279\u5fb4\u7684\u306a\u30b7\u30fc\u30b1\u30f3\u30b9\u3068\u3057\u3066\u8868\u793a\u3055\u308c\u307e\u3059\u3002 \u305d\u306e\u5f62\u306e\u305f\u3081 \uff08 22r+1 – \u521d\u3081 \uff09\uff09 de 2 2 r {displayStyle\u5de6\uff082^{2r+1} -1right\uff09cdot 2^{2r}} \u306e\u7d50\u679c\u3068\u3057\u3066\u3001\u6570\u5024\u30b7\u30b9\u30c6\u30e0\u306e4\u756a\u306b\u7acb\u3063\u3066\u3044\u307e\u3059 \u521d\u3081 {displaystyle1} \u540c\u3058\u304f\u3001 r {displaystyle r} 3\u3064\u3068 r {displaystyle r} \u30bc\u30ed\u30b9\u30c0\u30fc\u30eb\uff1a 28 = 130 4{displayStyle 28 = 130_ {4}} 496 = 13300 4{displaystyle 496 = 13300_ {4}} 8128 = 1333000 4{displaystyle 8128 = 1333000_ {4}} 33550336 = 1333333000000 4{displaystyle 33550336 = 13333330000_ {4}}} \u4e00 k {displaystyle k} – \u57fa\u672c\u7684\u306b\u306f\u6570\u5b57\u3067\u3042\u308a\u3001\u305d\u308c\u3089\u306e\u80af\u5b9a\u7684\u306a\u9664\u6570\u306e\u5408\u8a08\u306f\u3001\u6570\u5b57\u81ea\u4f53\u3088\u308a\u3082\u5c0f\u3055\u3044\u3001 k {displaystyle k} – \u6570\u5b57\u81ea\u4f53\u306e\u7d50\u679c\u304c\u5f97\u3089\u308c\u307e\u3059\u3002\u5b8c\u74a7\u306a\u6570\u5b57\u306f\u307e\u3055\u306b\u305d\u308c\u3067\u3059 \u521d\u3081 {displaystyle1} – \u57fa\u672c\u7684\u306b\u3002\u5168\u3066 k {displaystyle k} – \u5e0c\u671b\u8005\u306e\u6570\u5b57 k \u2265 2 {displaystyle kgeq 2} \u4e9b\u7d30\u306a\u3001\u8c4a\u5bcc\u306a\u6570\u5b57\u3067\u3059\u3002 \u4f8b\uff1a 120\u306b\u306f\u3001\u56f31\u30012\u30013\u30014\u30015\u30016\u30018\u300110\u300115\u300120\u300124\u300130\u300140\u3001\u304a\u3088\u307360\u304c\u3042\u308a\u307e\u3059\u3002 240 = 2 de 120 {displaystyle 240 = 2cdot 120} \u3001120\u500b\u3067 2 {displaystyle 2} – \u5b8c\u5168\u306a\u756a\u53f7\u3067\u3059\u3002 \u8c4a\u5bcc\u3067\u4e0d\u5341\u5206\u306a\u6570 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u8c4a\u5bcc\u306a\u6570\u306f\u305d\u306e\u3088\u3046\u306a\u81ea\u7136\u6570\u3067\u3059 n {displaystyle n} \u5b9f\u969b\u306e\u4ed5\u5207\u308a\u306e\u5408\u8a08 a \u2217 \uff08 n \uff09\uff09 {displaystyle sigma ^{*}\uff08n\uff09} \u6570\u81ea\u4f53\u3088\u308a\u3082\u5927\u304d\u3044\u3002\u4e0d\u8db3\u3057\u3066\u3044\u308b\u6570\u306f\u3001\u3053\u306e\u5408\u8a08\u304c\u6570\u81ea\u4f53\u3088\u308a\u3082\u5c0f\u3055\u3044\u81ea\u7136\u6570\u3067\u3059\u3002 \u6700\u5c0f\u306e\u8c4a\u5bcc\u306a\u6570\u306f12\u756a\u76ee\u3067\u3059\u3002 \u521d\u3081 + 2 + 3 + 4 + 6 = 16 {displaystyle 1+2+3+4+6 = 16} \u3002 100\u307e\u3067\u306e\u8c4a\u5bcc\u306a\u6570\u5b57\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002 12\u300118\u300120\u300124\u300130\u300136\u300140\u300142\u300148\u300154\u300156\u300160\u300166\u300170\u300172\u300178\u300180\u300184\u300188\u300190\u300196\u3001…\uff08\u30a8\u30d4\u30bd\u30fc\u30c9 A005101 OEIS\u3067\uff09 \u4e0d\u8db3\u3057\u305f\u6570\u5b57\u306f\u307b\u3068\u3093\u3069\u3059\u3079\u3066\u306e\u4eba\u3067\u3059\uff1a 1\u30012\u30013\u30014\u30015\u30017\u30018\u30019\u300111\u300114\u300115\u300116\u300117\u300119\u300121\u300122\u300123\u300126\u300127\u300129\u300131\u300133\u300134\u300135\u300137\u300138\u300139\u3001 A005100 OEIS\u3067\uff09 \u6570\u5b57\u304c\u8c4a\u5bcc\u3067\u3082\u4e0d\u8db3\u3057\u3066\u3044\u306a\u3044\u5834\u5408\u3001\u305d\u308c\u306f\u5b8c\u5168\u306a\u6570\u5b57\u3067\u3059\u3002 \u53cb\u9054\u306e\u53cb\u9054\u3068\u5384\u4ecb\u306a\u6570\u5b57 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u5b9f\u969b\u306e\u4ed5\u5207\u308a\u306e\u5408\u8a08\u304c\u3042\u308b2\u3064\u306e\u7570\u306a\u308b\u81ea\u7136\u6570 a \u2217 {displaystyle sigma ^{*}} \u6700\u521d\u306e\u6570\u5b57\u306f2\u756a\u76ee\u3067\u30012\u756a\u76ee\u306e\u6570\u5b57\u306f\u6700\u521d\u306e\u6570\u5b57\u3067\u30012\u3064\u306e\u6570\u5b57\u3068\u547c\u3070\u308c\u307e\u3059\u3002\u305d\u308c\u3089\u306e\u5c0f\u3055\u3044\u307b\u3069\u8c4a\u5bcc\u3067\u3001\u5927\u304d\u3044\u3082\u306e\u306f\u4e0d\u8db3\u3057\u3066\u3044\u307e\u3059\u3002 \u4f8b\uff1a 220 = a \u2217\uff08 284 \uff09\uff09 {displaystyle 220 = sigma ^{*}\uff08284\uff09} \u3068 284 = a \u2217\uff08 220 \uff09\uff09 {displaystyle 284 = sigma ^{*}\uff08220\uff09} \u6700\u5c0f\u306e\u30ab\u30c3\u30d7\u30eb\u306e\u53cb\u4eba\u3092\u5f62\u6210\u3057\u307e\u3059\u3002 \u3053\u306e\u65b9\u6cd5\u3067\u521d\u671f\u6570\u306b\u623b\u308b\u305f\u3081\u306b2\u3064\u4ee5\u4e0a\u306e\u81ea\u7136\u6570\u304c\u5fc5\u8981\u306a\u5834\u5408\u30011\u3064\u306f\u793e\u4ea4\u7684\u306a\u4eba\u7269\u306b\u3064\u3044\u3066\u8a71\u3057\u307e\u3059\u3002 \u793e\u4ea4\u7684\u306a\u6570\u5b57 \uff09\u3002 5\u3064\u306e\u793e\u4ea4\u7684\u306a\u6570\u5b57\u306e\u4f8b\uff1a 12,496\u300114,288\u300115,472\u300114,536\u300114,264 \u64ec\u4f3c\u30d5\u30a3\u30ae\u30e5\u30a2 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u81ea\u7136\u6570 n {displaystyle n} \u547c\u3070\u308c\u3066\u3044\u307e\u3059 Pseudovollkom\u3001 \u3042\u306a\u305f\u304c\u5408\u8a08\u3067\u3042\u308b\u5834\u5408 \u3044\u304f\u3064\u304b\u306e \u3055\u307e\u3056\u307e\u306a\u5b9f\u969b\u306e\u9664\u6570\u3067\u8868\u73fe\u3067\u304d\u307e\u3059\u3002 \u4f8b\uff1a 20 = \u521d\u3081 + 4 + 5 + \u5341 {displaystyle 20 = 1+4+5+10} \u64ec\u4f3c\u3067\u3044\u3063\u3071\u3044\u3067\u3059\u304c\u3001\u6982\u8981\u30c7\u30a3\u30b9\u30d7\u30ec\u30a4\u306b\u5206\u52722\u304c\u6b20\u843d\u3057\u3066\u3044\u308b\u305f\u3081\u3001\u5b8c\u74a7\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002 \u3059\u3079\u3066\u306e\u64ec\u4f3c\u7684\u306a\u6570\u5b57\u306f\u5b8c\u5168\u3067\u3042\u308b\u304b\u8c4a\u5bcc\u3067\u3059\u3002 \u64ec\u4f3c – \u5b8c\u5168\u306b\u5f62\u6210\u3055\u308c\u305f\u30d5\u30a3\u30ae\u30e5\u30a2\u306e\u5b9f\u969b\u306e\u30b5\u30d6\u30bb\u30c3\u30c8\u306f \u4e3b\u306b\u64ec\u4f3c\u30d5\u30a7\u30c3\u30c9\u30d5\u30a3\u30ae\u30e5\u30a2 \uff1a \u591a\u5206 n {displaystyle n} \u8907\u5408\u756a\u53f7\u3068 p {displaystyle p} \u306e\u4e3b\u8981\u306a\u9664\u6570\u306e\u91cf n {displaystyle n} \u3002\u4eba\u6570\u3001\u500b\u6570\u3001\u7dcf\u6570 n {displaystyle n} \u4e3b\u306b\u64ec\u4f3c\u3092\u53d6\u5f97\u3059\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002 n = \u521d\u3081 + \u2211 p\u2208Pnp{displaystyle n = 1+sum _ {battery p} {frac {n} {p}}}}} \u6b21\u306e\u7279\u6027\u8a55\u4fa1\u306f\u540c\u7b49\u3067\u3059\u3002\u8907\u5408\u756a\u53f7 n {displaystyle n} \u30d7\u30e9\u30a4\u30e0\u30c7\u30a3\u30d0\u30a4\u30c0\u30fc\u306e\u91cf p {displaystyle p} \u4e3b\u306b\u64ec\u4f3c – \u3057\u305f\u304c\u3063\u3066\u3001\u4ee5\u4e0b\u304c\u9069\u7528\u3055\u308c\u308b\u5834\u5408\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002 \u2211 p \u2208 p \u521d\u3081 p + \u220f p \u2208 p \u521d\u3081 p = \u521d\u3081 {displaystyle sum _ {pin p} {frac {1} {p}}+prod _ {pin p} {frac {1} {p}} = 1} \u3002\u3053\u308c\u306f\u3001\u4e3b\u306b\u64ec\u4f3c\u3055\u308c\u305f\u6570\u5b57\u306e\u5bc6\u63a5\u306a\u95a2\u4fc2\u306b\u3088\u3063\u3066\u793a\u3055\u308c\u3066\u3044\u307e\u3059\u3002 \u2211 p \u2208 p \u521d\u3081 p – \u220f p \u2208 p \u521d\u3081 p \u2208 n {displaystyle sum _ {pin p} {frac {1} {p}} – prod _ {pin p} {frac {1} {p}} in mathbb {n}} \u7279\u5fb4\u4ed8\u3051\u3089\u308c\u307e\u3059\u3002 \u65e2\u77e5\u306e\u6700\u3082\u65e2\u77e5\u306e\u6570\u5b57\u306f\u4e3b\u306b\u64ec\u4f3c\u7684\u3067\u3059\uff08\u7d50\u679c\uff09 A054377 OEIS\u3067\uff09\uff1a 2 = 2 6 = 2\u00d73 42 = 2\u00d73\u00d77 1806 = 2\u00d73\u00d77\u00d743 47.058 = 2\u00d73\u00d711\u00d723\u00d731 2.214.502.422 = 2\u00d73\u00d711\u00d723\u00d737.059 52.495.396.602 = 2\u00d73\u00d711\u00d717\u00d7101\u00d7149\u00d73109 8.490.421.583.559.688.410.706.771.771.086 = 2\u00d73\u00d711\u00d711\u00d723\u00d731\u00d747.059\u00d72,217.342.227\u00d71,729.101.023.519.519.519.519.519 \u305d\u308c\u304b\u3069\u3046\u304b\u306f\u4e0d\u660e\u3067\u3059 \u591a\u304f\u306e\u4eba \u4e3b\u306b\u64ec\u4f3c – \u3057\u3063\u304b\u308a\u3068\u6765\u308b\u304b\u3001\u3042\u308b\u304b\u3069\u3046\u304b \u5947\u6570 \u4e3b\u8981\u306a\u64ec\u4f3c\u8b58\u529b\u6570\u3002 \uff08\uff08\uff09 A054377 \uff09\uff09 \u4e3b\u306b\u64ec\u4f3c\u3055\u308c\u305f\u6570\u5b57\u306e\u7279\u6027\uff1a \u3059\u3079\u3066\u4e3b\u306b\u64ec\u4f3c\u30d5\u30a7\u30c3\u30c9\u6570\u306f\u6b63\u65b9\u5f62\u3067\u3059\u3002 \u30ca\u30f3\u30d0\u30fc6\u306f\u3001\u4e3b\u306b\u552f\u4e00\u306e\u64ec\u4f3c\u30d5\u30a7\u30c9\u756a\u53f7\u3067\u3042\u308a\u3001\u3053\u308c\u3082\u5b8c\u4e86\u3057\u3066\u3044\u307e\u3059\u3002\u4ed6\u306e\u3059\u3079\u3066\u306e\u4e3b\u306b\u64ec\u4f3c\u30d5\u30a7\u30c9\u6570\u306f\u8c4a\u5bcc\u3067\u3059\u3002 \u4e3b\u306b\u64ec\u4f3c\u30d5\u30a7\u30c9\u6570\u304c\u591a\u304f\u3001\u7279\u5b9a\u306e\u6570\u306e\u4e3b\u8981\u306a\u8981\u56e0\u304c\u3042\u308a\u307e\u3059\u3002 \u4e3b\u306b\u64ec\u4f3c\u30d5\u30a7\u30c3\u30c9\u306e\u6570\u5b57\u304c\u7121\u9650\u306b\u3042\u308b\u304b\u3069\u3046\u304b\u306f\u4e0d\u660e\u3067\u3059\u3002 \u5947\u5999\u306a\u6570\u5b57\u3084\u5947\u5999\u306a\u6570\u5b57 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u81ea\u7136\u6570 n {displaystyle n} \u547c\u3070\u308c\u3066\u3044\u307e\u3059 \u5909 \uff08\u30c9\u30a4\u30c4\u8a9e\u3067\u306f\u3001\u300c\u5947\u5999\u306a\u300d\uff09\u8c4a\u5bcc\u3067\u306f\u306a\u3044\u304c\u3001\u64ec\u4f3c\u3067\u306f\u306a\u3044\u5834\u5408\u3002\u305d\u306e\u305f\u3081\u3001\u5b9f\u969b\u306e\u9664\u6570\u306e\u5408\u8a08\u306f\u6570\u5b57\u3067\u3059\u304c\u3001\u305d\u306e\u5b9f\u969b\u306e\u9664\u6570\u306e\u3044\u304f\u3064\u304b\u306e\u5408\u8a08\u3068\u3057\u3066\u8868\u73fe\u3059\u308b\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u3002 n {displaystyle n} \u8d85\u3048\u3066\u3002 \u4f8b\uff1a\u6570\u5b5770\u306f\u6700\u5c0f\u306e\u5947\u5999\u306a\u6570\u3067\u3059\u3002\u305d\u308c\u306f\u90e8\u9580\u304b\u3089\u306e\u6570\u5b57\u306e\u5408\u8a08\u3067\u306f\u3042\u308a\u3048\u307e\u305b\u3093 { \u521d\u3081 \u3001 2 \u3001 5 \u3001 7 \u3001 \u5341 \u3001 14 \u3001 35 } {displaystyle {1,2,5,7,10,14,35}} \u66f8\u304f\u3002\u6b21\u306e\u5947\u5999\u306a\u6570\u5b57\u306f836\u30014030\u30015830\u30017192\u30017912\u30019272\u300110430\u3067\u3059\uff08\u7d50\u679c A006037 OEIS\u3067\uff09 \u7279\u6027\uff1a \u5947\u5999\u306a\u6570\u306e\u7121\u9650\u306e\u6570\u304c\u3042\u308a\u307e\u3059\u3002 \u65e2\u77e5\u306e\u5947\u5999\u306a\u6570\u5b57\u306f\u3059\u3079\u3066\u307e\u3063\u3059\u3050\u3067\u3059\u3002\u5947\u5999\u306a\u5947\u5999\u306a\u6570\u304c\u3042\u308b\u304b\u3069\u3046\u304b\u306f\u4e0d\u660e\u3067\u3059\u3002 seried\u756a\u53f7 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u90e8\u54c1\u6570\u3068\u81ea\u7136\u6570\u306e\u9664\u6570\u306e\u5408\u8a08\u306e\u4e21\u65b9\u3067\u3059 n {displaystyle n} \u5b8c\u74a7\u306a\u6570\u5b57\u3001\u6b21\u306b1\u3064\u3092\u793a\u3057\u307e\u3059 n {displaystyle n} \u3044\u3064 \u4e0a\u3052\u3089\u308c\u305f\u3002 \u5f53\u6642\uff082010\u5e74\uff09\u5d07\u9ad8\u306a\u6570\u5b57\u306f2\u3064\u306e\u5d07\u9ad8\u306a\u6570\u306e\u307f\u3067\u3059\u300212\u306876\u306e\u30b8\u30e7\u30d6\u306e\u6570\u5b57\uff08\u7d50\u679c A081357 OEIS\u3067\uff09\u3002 \u6e96\u7570\u306a\u308b\u6570\u5b57 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u6e96\u7570\u306a\u308b\u6570\u5b57 \uff08 \u82f1\u8a9e quasiperfect\u6570 \uff09\u5b8c\u5168\u306a\u6570\u5b57\u306e\u660e\u3089\u304b\u306a\u5909\u66f4\u3068\u3057\u3066\u306e\u7d50\u679c\u3002\u3053\u308c\u3092\u884c\u3046\u306b\u306f\u3001\u90e8\u54c1\u306e\u5168\u91cf\u3067\u306f\u306a\u304f\u81ea\u7136\u6570\u3092\u53d6\u5f97\u3057\u307e\u3059 n {displaystyle n} \u305d\u308c\u3060\u3051\u3067 \u975e\u4e9b\u7d30\u306a\u4ed5\u5207\u308a\u3001 \u3057\u305f\u304c\u3063\u3066\u3001\u3059\u3079\u3066\u306e\u30d1\u30fc\u30c8\u30ca\u30fc\u3092\u9664\u304f \u521d\u3081 {displaystyle1} \u3068 n {displaystyle n} \u305d\u308c\u81ea\u4f53\u3001\u305d\u3057\u3066\u305d\u308c\u3089\u306e\u5408\u8a08\u304c\u6570\u306b\u7b49\u3057\u3044\u3053\u3068\u3092\u8981\u6c42\u3057\u307e\u3059 n {displaystyle n} \u591a\u5206\u3002 a n \u2208 n {displaystyle nin mathbb {n}} \u3057\u305f\u304c\u3063\u3066\u3001\u307e\u3055\u306b\u305d\u3046\u3067\u3059 \u98a8\u6587\u3001 \u65b9\u7a0b\u5f0f\u306e\u5834\u5408 a \uff08 n \uff09\uff09 = 2 n + \u521d\u3081 {displaystyle sigma\uff08n\uff09= 2n+1} \u6e80\u8db3\u3057\u3066\u3044\u307e\u3059\u3002 \u3053\u308c\u307e\u3067\u306e\u3068\u3053\u308d\uff082006\u5e74\u73fe\u5728\uff09\u3001Quasi -wund\u6570\u306f\u308f\u304b\u3063\u3066\u3044\u307e\u305b\u3093\u3002\u6b21\u306e\u3088\u3046\u306a\u3001\u3059\u3079\u3066\u306e\u6e96\u6570\u5024\u3092\u6e80\u305f\u3059\u5fc5\u8981\u304c\u3042\u308b\u591a\u304f\u306e\u5fc5\u8981\u306a\u6761\u4ef6\u3057\u304b\u898b\u3064\u304b\u308a\u307e\u305b\u3093\u3067\u3057\u305f\u3002 [2] [9] [\u5341] SuperPerfects\u3092\u652f\u6255\u3044\u307e\u3059 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u3042\u306a\u305f\u304c\u81ea\u7136\u6570\u306e\u5206\u5272\u306e\u30b7\u30a7\u30a2\u304b\u3089\u6301\u3063\u3066\u3044\u308b\u306a\u3089 n {displaystyle n} \u90e8\u9580\u306e\u30b7\u30a7\u30a2\u3092\u518d\u5f62\u6210\u3057\u3001\u3053\u306e\u7b2c2\u984d\u306e\u90e8\u9580\u306f2\u500d\u306e\u5927\u304d\u3055\u3067\u3059 n {displaystyle n} \u3001 \u307e\u305f a \uff08 a \uff08 n \uff09\uff09 \uff09\uff09 = 2 de n {displaystyle sigma\uff08sigma\uff08n\uff09\uff09= 2cdot n} \u9069\u7528\u3057\u3066\u304b\u3089\u30011\u3064\u306e\u547c\u3073\u51fa\u3057\u3092\u884c\u3044\u307e\u3059 n {displaystyle n} \u975e\u5e38\u306b\u904e\u5270\u306a\u6570\uff08\u7d50\u679c A019279 OEIS\u3067\uff09\u3002 \u4f8b \u30dc\u30a8\u30c6\u30a3\u30a6\u30b9 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u5b8c\u5168\u306a\u6570\u306e\u7b97\u8853\u7279\u6027\u3001\u6642\u306b\u306f\u305d\u308c\u3089\u306e\u7b97\u8853\u7684\u89e3\u91c8\u306f\u3001\u53e4\u4ee3\u5f8c\u671f\u306e\u7b97\u8853\u6559\u80b2\u8cc7\u6599\u306e\u4e00\u90e8\u3067\u3042\u308a\u3001\u305d\u306e\u4e2d\u306e\u30dc\u30a8\u30c6\u30a3\u30a6\u30b9\u3067\u3059 \u5f93\u6765\u306e\u7b97\u8853 [11] \u305d\u308c\u306f\u4e3b\u306b\u30b8\u30a7\u30e9\u30b5\u30fb\u30cb\u30b3\u30de\u30b3\u30b9\u306b\u57fa\u3065\u3044\u3066\u3044\u307e\u3059\u3001 [12\u756a\u76ee] \u30e9\u30c6\u30f3\u4e2d\u4e16\u306b\u6e21\u3055\u308c\u307e\u3057\u305f\u3002\u5f7c\u306e\u30ae\u30ea\u30b7\u30e3\u306e\u30c6\u30f3\u30d7\u30ec\u30fc\u30c8\u306b\u5f93\u3063\u3066\u3001\u30dc\u30a8\u30c6\u30a3\u30a6\u30b9\u306f\u5b8c\u74a7\u306a\u6570\u5b57\u3092\u6271\u3063\u3066\u3044\u307e\u3059 \uff08\u5b8c\u6210\u3057\u305f\u90e8\u54c1\u306e\u6570\uff09 [13] \u30b9\u30c8\u30ec\u30fc\u30c8\u6570\u306e\u4e9c\u7a2e\u3068\u3057\u3066 \uff08\u6570\u5b57\uff09 \u305d\u3057\u3066\u3001\u30e1\u30f3\u30d0\u30fc\u304c\u4e00\u9023\u306e\u76f4\u7dda\u3067\u652f\u6255\u3046\u3088\u3046\u306a\u65b9\u6cd5\u3067\u3001\u3042\u306a\u305f\u306e\u8a08\u7b97\u539f\u5247\u3092\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u306b\u623b\u3059\u3053\u3068\u3092\u8aac\u660e\u3057\u307e\u3059\uff08 \u6570\u5b57\u3060\u3051\u3067\u306a\u304f\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 2 n \uff09\u5408\u8a08\u304c\u7d20\u6570\u3092\u4e0e\u3048\u308b\u307e\u3067\u4e92\u3044\u306b\u8ffd\u52a0\u3059\u308b\u3053\u3068\uff1a\u3053\u306e\u7d20\u6570\u3092\u6700\u5f8c\u306b\u8ffd\u52a0\u3057\u305f\u30b7\u30ea\u30fc\u30ba\u306b\u639b\u3051\u308b\u3068\u3001\u5b8c\u74a7\u306a\u6570\u304c\u3042\u308a\u307e\u3059\u3002 Bo\u00ebthius\u306f\u3001\u6700\u521d\u306e3\u3064\u306e\u5b8c\u5168\u306a\u6570\u5b576\u300128\u3001\u304a\u3088\u3073496\u306e\u500b\u3005\u306e\u30b9\u30c6\u30c3\u30d7\u3067\u3053\u306e\u8a08\u7b97\u65b9\u6cd5\u3092\u30ea\u30fc\u30c9\u3057\u30014\u756a\u76ee\u306e\u5b8c\u5168\u306a\u6570\u5b578128\u306b\u3064\u3044\u3066\u3082\u8a00\u53ca\u3057\u3066\u3044\u307e\u3059\u3002\u30dc\u30a8\u30c6\u30a3\u30a6\u30b9\u3067\u306f\u3001\u5b8c\u74a7\u306a\u6570\u5b57\u306e\u5408\u6cd5\u6027\u306e\u88dc\u5b8c\u7684\u306a\u89b3\u5bdf\u306f\u300110\u5e74\u3054\u3068\u306b1\u56de\uff08\u6642\u9593\u306e\u52b9\u529b\uff09\u306b\u4e00\u5ea6\u767b\u5834\u3057\u30016\u307e\u305f\u306f8\u3067\u7d42\u4e86\u3057\u305f\u3053\u3068\u306b\u3082\u57fa\u3065\u3044\u3066\u3044\u307e\u3059\u3002 Bo\u00ebthius\u306e\u8aac\u660e\u306f\u3001\u6b21\u306e\u4e16\u7d00\u306b\u5b8c\u5168\u306a\u6570\u5b57\u306b\u95a2\u3059\u308b\u7b97\u8853\u77e5\u8b58\u306e\u5408\u8a08\u3092\u5f62\u6210\u3057\u307e\u3057\u305f \u7b97\u8853\u306e \u306a\u3069\u306e\u767e\u79d1\u4e8b\u5178\u3067 Etymologiae ISIDORS [14] \u305d\u3057\u3066\u3001\u4ed6\u306e\u6559\u8a13\u7684\u306a\u4f5c\u54c1\u306f\u591a\u304b\u308c\u5c11\u306a\u304b\u308c\u5b8c\u5168\u3067\u3057\u305f\u304c\u300115\u4e16\u7d00\u306b5\u756a\u76ee\u306e\u5b8c\u5168\u306a\u6570\uff0833550336\uff09\u304c\u767a\u898b\u3055\u308c\u308b\u307e\u3067\u3001\u300c\u6570\u5341\u5e74\u300d\u3078\u306e\u901a\u5e38\u306e\u5206\u5e03\u306b\u95a2\u3059\u308b\u4eee\u5b9a\u304c\u4e0d\u6b63\u78ba\u3067\u3042\u308b\u3053\u3068\u304c\u8a8d\u8b58\u3055\u308c\u3066\u3044\u307e\u3057\u305f\u3002 [15] Bo\u00ebthius\u306f\u3001\u4ed6\u306e\u6570\u306e\u6570\u306e\u6cbb\u7642\u306b\u304a\u3051\u308b\u7b97\u8853\u6559\u80b2\u8cc7\u6599\u306b\u5927\u304d\u304f\u9650\u5b9a\u3055\u308c\u3066\u3044\u307e\u3059\u304c\u3001\u5b8c\u5168\u306a\u6570\u5b57\u306f\u3001\u305d\u308c\u3089\u304c\u8c4a\u5bcc\u3067\u3042\u308b\u3068\u3044\u3046\u3055\u3089\u306a\u308b\u502b\u7406\u7684\u8003\u616e\u4e8b\u9805\u306e\u7406\u7531\u3092\u5f7c\u306b\u63d0\u4f9b\u3057\u307e\u3059\uff08 \u5b8c\u74a7\u4ee5\u4e0a\u306e\u3082\u306e \u307e\u305f \u4f59\u5206\u306a \u307e\u305f \u8c4a\u5bcc\u3067\u3059 \u540d\u524d\u4ed8\u304d\uff09\u304a\u3088\u3073\u8d64\u5b57\u6570\uff08 \u4e0d\u5b8c\u5168 \u307e\u305f \u5c0f\u3055\u3044 \u307e\u305f \u30db\u30fc\u30e0\u30ec\u30b9 \u540d\u524d\uff09\u3068\u6bd4\u8f03\u3055\u308c\u307e\u3059\uff1a\u3053\u308c\u3089\u306e\u5f8c\u8005\u306e2\u7a2e\u985e\u306e\u6570\u5b57\u306f\u3001\u305d\u308c\u3089\u304c\u975e\u5e38\u306b\u4e00\u822c\u7684\u3067\u3001\u305d\u308c\u3089\u306e\u3088\u3046\u306b\u4e00\u822c\u7684\u3067\u3042\u308a\u3001\u7279\u5b9a\u306e\u9806\u5e8f\u306b\u63d0\u51fa\u3057\u306a\u3044\u305f\u3081\u3001\u4eba\u9593\u306e\u30c8\u30e9\u30c3\u30af\u306b\u4f3c\u3066\u3044\u307e\u3059\u304c\u3001\u632f\u308b\u821e\u3044\u307e\u3059 \u5b8c\u74a7\u306a\u6570\u5b57 \u7f8e\u5fb3\u306e\u3088\u3046\u306b\u3001\u6b63\u3057\u3044\u5c3a\u5ea6\u3092\u7dad\u6301\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u904e\u5270\u3068\u6b20\u5982\u306e\u9593\u306e\u771f\u3093\u4e2d\u306f\u975e\u5e38\u306b\u307e\u308c\u306b\u898b\u3089\u308c\u305a\u3001\u56fa\u5b9a\u9806\u5e8f\u306b\u63d0\u51fa\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u30dc\u30a8\u30c6\u30a3\u30a6\u30b9\u306f\u307e\u305f\u30013\u4eba\u306e\u30e1\u30f3\u30d0\u30fc\u306e\u30b2\u30ea\u30aa\u30f3\u306a\u3069\u306e\u795e\u8a71\u306e\u30e2\u30f3\u30b9\u30bf\u30fc\u3068\u8c4a\u304b\u3055\u3092\u6bd4\u8f03\u3059\u308b\u3068\u3001\u5b8c\u5168\u306a\u6570\u5b57\u306b\u5bfe\u3059\u308b\u7f8e\u7684\u597d\u307f\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u304c\u3001\u5f7c\u306f\u4e0d\u8db3\u3057\u3066\u3044\u308b\u3053\u3068\u3092\u5909\u5f62\u3068\u6bd4\u8f03\u3057\u307e\u3059\u3002\u30dc\u30a8\u30c6\u30a3\u30a6\u30b9\u304c\u5f7c\u306e\u30ae\u30ea\u30b7\u30e3\u306e\u30c6\u30f3\u30d7\u30ec\u30fc\u30c8\u304b\u3089\u3059\u3067\u306b\u53d6\u3063\u3066\u3044\u308b\u3053\u308c\u3089\u306e\u6bd4\u8f03\u306e\u5834\u5408\u3001\u305d\u306e\u30a2\u30a4\u30c7\u30a2\u306f\u624b\u8db3\u304b\u3089\u306e\u30ca\u30f3\u30d0\u30fc\u30ef\u30f3\u306e\u80cc\u666f\u306b\u3042\u308a\u307e\u3059 \uff08\u90e8\u54c1\uff09 \u8907\u5408 \u4f53 \u305d\u306e\u305f\u3081\u3001\u6570\u306e\u624b\u8db3\u306f\u3001\u5b8c\u5168\u306a\u6570\u3067\u3042\u306a\u305f\u306e\u4f53\u3068\u306e\u30d0\u30e9\u30f3\u30b9\u306e\u3068\u308c\u305f\u95a2\u4fc2\u306b\u3042\u308b\u3088\u3046\u306b\u3057\u3066\u3044\u307e\u3059\u3002 \u30d0\u30a4\u30d6\u30ec\u30ad\u30bb\u30fc\u30bc [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u4e2d\u4e16\u306e\u4f1d\u7d71\u306b\u5bfe\u3059\u308b\u5f7c\u3089\u306e\u5b9f\u969b\u306e\u91cd\u8981\u6027\u306f\u3001\u795e\u304c\u5f7c\u306e\u5275\u9020\u306e\u4f5c\u54c1\u3092\u5b8c\u6210\u3055\u305b\u305f6\u65e5\u9593\u306e\u5275\u9020\u306e\u89e3\u91c8\uff08vetus latina\u306e\u300c\u6d88\u8cbb\u8005\u300d\u3001\u300chieronymus\u306evulga\u300d\u306e\u300cperfecit “\uff09\u304c\u3001\u30a2\u30ea\u30c8\u30e9\u30b7\u7cfb\u306e\u9593\u306e\u51fa\u767a\u70b9\u3092\u5f62\u6210\u3059\u308b\u8056\u66f8\u89e3\u91c8\u3067\u5b8c\u74a7\u306a\u6570\u3092\u767a\u5c55\u3055\u305b\u307e\u3057\u305f\u3002 \u5b8c\u74a7 \u795e\u306e\u5275\u9020\u7269\u306e6\u3064\u306e\u30ca\u30f3\u30d0\u30fc\u3068\u5b8c\u74a7\u3055\u306f\u3001\u3064\u306a\u304c\u308b\u305f\u3081\u306b\u50cd\u304d\u307e\u3059\u3002 [16] \u3053\u306e\u4f1d\u7d71\u3067\u306f\u30016\u4eba\u306e\u6570\u5b57\u306f\u3001\u795e\u306e\u5275\u9020\u7269\u304c\u5f8c\u306e\u30a4\u30e9\u30b9\u30c8\u306e\u5178\u578b\u7684\u306a\u4f8b\u3067\u3057\u305f\u3002 \u6e2c\u5b9a\u3001\u6570\u3001\u91cd\u91cf \u6ce8\u6587\u3055\u308c\u307e\u3059\u3002\u30e9\u30c6\u30f3\u754c\u306e\u6c7a\u5b9a\u7684\u306a\u8981\u56e0\u306f\u30a2\u30a6\u30b0\u30b9\u30c6\u30a3\u30cc\u30b9\u306b\u306a\u308a\u3001\u30a2\u30a6\u30b0\u30b9\u30c6\u30a3\u30cc\u30b9\u306f\u3055\u3089\u306b\u30a2\u30ec\u30af\u30b5\u30f3\u30c9\u30ea\u30f3\u306e\u89e3\u91c8\u304b\u3089\u524d\u4efb\u8005\u304b\u3089\u3055\u3089\u306b\u958b\u767a\u3055\u308c\u307e\u3057\u305f\u3002\u30a2\u30a6\u30b0\u30b9\u30c6\u30a3\u30cc\u30b9\u306f\u975e\u5e38\u306b\u983b\u7e41\u306b\u3042\u308a\u307e\u3059 \u5b8c\u74a7 \u5f7c\u306e\u30b3\u30e1\u30f3\u30c8\u306e\u4e2d\u3067\u6700\u3082\u8a73\u7d30\u306a6\u3064\u306e\u30ca\u30f3\u30d0\u30fc\u306e\u3046\u3061 \u5275\u4e16\u8a18\u306e\u624b\u7d19 [17] \u5f7c\u304c\u7b97\u8853\u7684\u4e8b\u5b9f\u3092\u8aac\u660e\u3059\u308b\u3060\u3051\u3067\u306a\u304f\u3001\u795e\u5b66\u7684\u306a\u8cea\u554f\u306f\u3001\u795e\u304c\u5f7c\u3089\u306e\u5b8c\u74a7\u3055\u306e\u305f\u3081\u306b6\u3064\u306e\u6570\u5b57\u3092\u9078\u3093\u3060\u306e\u304b\u3001\u305d\u308c\u3068\u3082\u5f7c\u306e\u9078\u629e\u3092\u901a\u3057\u3066\u3053\u306e\u5b8c\u5168\u6027\u3092\u4e0e\u3048\u305f\u306e\u304b\u3092\u8b70\u8ad6\u3057\u307e\u3059\u304c\u3001\u5275\u9020\u690d\u7269\u3067\u3082\u5f7c\u3089\u306b\u3088\u3063\u30666\u3064\u306e\u6570\u5b57\u306e\u5145\u8db3\u611f\u304c\u5b9f\u8a3c\u3055\u308c\u307e\u3057\u305f\u3002 \u3042\u306a\u305f\u3078 \uff08\u30d1\u30fc\u30c6\u30a3\uff091\u30012\u30013\u306f\u3001\u5275\u9020\u4f5c\u54c1\u306e\u6027\u8cea\u3068\u6f5c\u5728\u6027\u306b\u3082\u53cd\u6620\u3055\u308c\u3066\u3044\u307e\u3059 \u6ce8\u6587 \u4f5c\u6210\u306f\u5bfe\u5fdc\u3057\u3066\u3044\u307e\u3059\uff1a \u5275\u9020\u306e\u5275\u9020\u306e\u521d\u65e5 \u30e9\u30a4\u30c8\u3001 \u305d\u308c\u306f\u3001\u30a2\u30a6\u30b0\u30b9\u30c6\u30a3\u30cc\u30b9\u306b\u3068\u3063\u3066\u3001\u5929\u56fd\u306e\u77e5\u6027\u306e\u5275\u9020\u3092\u6697\u793a\u3057\u3066\u3044\u308b\u3053\u3068\u3082\u3001 a \u305d\u308c\u81ea\u4f53\u306e\u305f\u3081\u306e\u65e5\u3002 \u5f7c\u3089\u306f\u5f7c\u306b\u5f93\u3063\u3066\u3044\u307e\u3059 \u4e8c \u4e16\u754c\u306e\u5efa\u7269\u306e\u65e5\u3001 \u30c7\u30d0\u30a4\u30b9\u306e\u4e16\u754c \u4f5c\u6210\u3055\u308c\u307e\u3057\u305f\uff1a\u5275\u9020\u306e2\u65e5\u76ee\u306b\u3001\u307e\u305a\u7b2c\u4e00\u306b \u4e0a\u5834\u3001 \u7a7a\u306e\u5927\u7a7a\u3001\u305d\u3057\u3066\u306e\u5275\u9020\u306e3\u65e5\u76ee \u3088\u308a\u4f4e\u3044\u30a8\u30ea\u30a2\u3001 \u4e7e\u71e5\u3057\u305f\u56fd\u3068\u6d77\u3002 \u6700\u5f8c \u4e09\u3064 \u305d\u308c\u81ea\u4f53\u304c\u4f5c\u6210\u3055\u308c\u305f\u30af\u30ea\u30fc\u30c1\u30e3\u30fc\u304c\u3053\u308c\u3067\u4f5c\u6210\u3055\u308c\u305f\u306e\u3067\u3001\u65e5\u3005\u306f\u518d\u3073\u30b0\u30eb\u30fc\u30d7\u3092\u5f62\u6210\u3057\u307e\u3059 \u30c7\u30d0\u30a4\u30b9\u306e\u4e16\u754cBewegen \u3042\u306a\u305f\u3082 \u5165\u529b\u3057\u307e\u3059 \u3068 \u98fe\u308b \u5fc5\u8981\uff1a4\u65e5\u76ee\u306b\u3001\u5929\u4f53\u3001\u592a\u967d\u3001\u6708\u3001\u661f\u30015\u65e5\u76ee\u306b \u4e0b\u90e8\u30a8\u30ea\u30a2 \u6c34\u3068\u7a7a\u6c17\u306e\u52d5\u7269\u3001\u305d\u3057\u30666\u65e5\u76ee\u306b\u6700\u7d42\u7684\u306b\u56fd\u306e\u52d5\u7269\u3068\u6700\u8fd1\u306e\u6700\u3082\u5b8c\u74a7\u306a\u4f5c\u54c1\u3002 \u30a2\u30a6\u30b0\u30b9\u30c6\u30a3\u30cc\u30b9\u304c\u4e09\u89d2\u5f62\u306e\u6570\u3068\u3057\u3066\u3082\u53d6\u308a\u7d44\u3093\u3067\u3044\u308b6\u3064\u306e\u6570\u306e\u5b8c\u74a7\u3055\u306f\u3001\u3053\u306e\u4e8b\u5b9f\u306e\u89e3\u91c8\u3092\u901a\u3057\u30662\u3064\u306e\u65b9\u6cd5\u3092\u3082\u305f\u3089\u3057\u307e\u3059\u3002\u4e00\u65b9\u3067\u306f\u3001 \u521d\u3081 + 2 + 3 {displaystyle 1+2+3} \u4e00\u65b9\u30011\u65e5\u76ee\u3067\u3059\u304c\u30011\u65e5\u76ee\u306e\u4f5c\u54c1\u304c\u7279\u5225\u306a\u4e0a\u90e8\u307e\u305f\u306f\u4e0b\u90e8\u306e\u9818\u57df\u306b\u5272\u308a\u5f53\u3066\u3089\u308c\u3066\u3044\u306a\u3044\u3068\u3044\u3046\u4e8b\u5b9f\uff08\u3053\u3053\u3067\u306f\u624b\u7d19a\u3067\u8c61\u5fb4\u3055\u308c\u307e\u3059\uff09\u3001\u4e00\u65b9\u3001\u4e0a\u90e8\uff08b\uff09\u307e\u305f\u306f\u4e0b\u90e8\uff08c\uff09\u306e\u9818\u57df\u306b\u5c5e\u3059\u308b\u305f\u3081\u30011\u30012\u30013\u65e5\u306e\u5b8c\u5168\u306a\u9806\u5e8f\u304c\u3042\u308a\u307e\u3059\u3002 a + b c + b c c {displaystyle a+bc+bcc} \u7d50\u679c\u3002 \u4e3b\u306b\u3001\u6f5c\u5728\u6027\u306e\u3053\u306e\u8a73\u7d30\u306a\u89e3\u91c8\u3067\u306f\u3042\u308a\u307e\u305b\u3093 \u6ce8\u6587\u3001 \u3057\u304b\u3057\u3001\u5c11\u306a\u304f\u3068\u3082\u7b97\u8853\u3068\u3057\u3066\u306e\u4e00\u822c\u7684\u306a\u89e3\u91c8\u3067\u306f \u756a\u53f7\u306f\u5b8c\u74a7\u3067\u3059 \u4e2d\u4e16\u306e\u89e3\u91c8\u306e\u4e00\u822c\u7684\u306a\u8cc7\u6599\u306e6\u3064\u306e\u30b9\u30c6\u30fc\u30b8\u3068\u3001\u8056\u66f8\u306b\u304a\u3051\u308b6\u3064\u306e\u6570\u5b57\u306e\u307b\u307c\u3059\u3079\u3066\u306e\u65b9\u6cd5\u306e\u89e3\u91c8\u3068\u6551\u3044\u306e\u6b74\u53f2\u306e\u89e3\u91c8\u306e\u51fa\u767a\u70b9\uff08\u30a2\u30c0\u30e0\u3001\u30ce\u30a2\u3001\u30ce\u30a2\u3001\u30a2\u30d6\u30e9\u30cf\u30e0\u3001\u30a2\u30d6\u30e9\u30cf\u30e0\u3001\u30c7\u30a4\u30d3\u30c3\u30c9\u3001\u30d0\u30d3\u30ed\u30cb\u30a2\u306e\u6355\u865c\u3001\u30ad\u30ea\u30b9\u30c8\uff09\u3092\u542b\u3080\u3001\u6551\u3044\u306e\u6b74\u53f2\u306e\u3053\u306e\u7406\u89e3\u306b\u306a\u308a\u307e\u3057\u305f\u3002 \uff08\u6cd5\u5f8b\u306e\u524d\uff09 3\u3064\u306e\u300c\u6cd5\u5f8b\u306e\u4e0b\u300d \uff08\u6cd5\u5f8b\u306e\u4e0b\uff09 \u305d\u3057\u3066\u6075\u307f\u306e\u6642\u4ee3\u3068\u3057\u3066 \uff08\u6075\u307f\u306e\u4e0b\uff09 \u30ad\u30ea\u30b9\u30c8\u306e\u60c5\u71b1\u306f\u3001\u4eba\u9593\u306e6\u6642\u4ee3\u306e\u89e3\u91c8\u3068\u30016\u65e5\u76ee\u304b\u3089\u306e6\u65e5\u76ee\u306e\u8056\u9031\u9593\u306e\u89e3\u91c8\u3068\u3001\u4ed6\u306e\u591a\u304f\u306e\u8056\u66f8\u304a\u3088\u3073\u975e\u8056\u66f8\u306e\u30bb\u30a2\u30ec\u3067\u89e3\u91c8\u3055\u308c\u307e\u3057\u305f\u3002 \u8a69 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u307e\u305f\u3001\u4e2d\u4e16\u306e\u8a69\u4eba\u306f\u307e\u305f\u3001\u5f7c\u306e\u8056\u66f8 – \u30a8\u30af\u30b9\u30da\u30b7 – \u5f7c\u3089\u306e\u4f5c\u54c1\u306e\u69cb\u9020\u306eegetic\u306a\u5185\u5bb9\u306b\u304a\u3051\u308b\u7b97\u8853\u7684\u7406\u89e3\u3092\u4f7f\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u3053\u308c\u3092\u78ba\u7acb\u3057\u307e\u3057\u305f\u3002 [18] \u30a2\u30eb\u30af\u30a4\u30f3\u306f\u3001\u30b0\u30f3\u30c9\u30e9\u30c0\u306e6\u7bc0\u306b6\u7bc0\u306b6\u3064\u306e\u30b9\u30bf\u30f3\u30b6\u3067\u30e1\u30c8\u30ea\u30c3\u30af\u8a69\u3092\u66f8\u304d\u3001\u5049\u5927\u306a\u30b7\u30e3\u30fc\u30ec\u30de\u30cb\u30e5\u306e\u89aarelative\u3067\u3042\u308b\u3002 \u5b8c\u74a7 \u53d7\u4fe1\u8005\u3092\u5ba3\u4f1d\u3059\u308b\u306b\u306f\uff1a [19] \u300c\u3053\u306e\u66f2\u306f\u3001\u5f7c\u3089\u306e\u90e8\u54c1\u306e\u6570\u306e\u6570\u306e\u53e4\u3044\u6570\u306e\u9ad8\u8cb4\u306a\u3082\u306e\u306b\u306a\u308b\u3067\u3057\u3087\u3046\u3002\u3042\u306a\u305f\u306f\u3042\u306a\u305f\u306e\u611f\u60c5\u306b\u304a\u3044\u3066\u5b8c\u74a7\u306b\u306a\u308a\u305f\u3044\u3067\u3059\u3002\u4ed6\u306e\u6570\u306e\u3088\u3046\u306b\u3001\u3042\u306a\u305f\u306e\u969c\u5bb3\u8005\u306e\u6700\u3082\u8ce2\u3044\u4eba\u306f\u3001agacity\u6027\u3092\u793a\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u300d \u300c\u79c1\u306f\u3053\u306e\u8a69\u3092\u30ce\u30fc\u30d6\u30eb\u30b7\u30c3\u30af\u30b9\u30ca\u30f3\u30d0\u30fc\u3067\u6b4c\u3044\u307e\u3057\u305f\u3002\u3053\u308c\u306f\u3042\u306a\u305f\u306e\u90e8\u5206\u3067\u5b8c\u74a7\u3067\u3059\u3002\u6700\u3082\u7687\u5e1d\u306f\u3042\u306a\u305f\u306e\u5b66\u7fd2\u306b\u8aac\u660e\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3067\u3057\u3087\u3046 – \u4ed6\u306e\u6570\u5b57\u3067\u305d\u308c\u304c\u4f55\u3067\u3042\u308b\u304b\u3092\u7c21\u5358\u306b\u8aac\u660e\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u300d – \u7ffb\u8a33\u8005P.\u30af\u30ed\u30d7\u30b7\u30e5 Alkuin\u306e\u5b66\u751fHrabanus Maurus\u306f\u3001\u3044\u304f\u3064\u304b\u306e\u77ed\u3044\u8a69\u3067\u540c\u69d8\u306e\u65b9\u6cd5\u3067\u305d\u306e\u3088\u3046\u306a\u95a2\u4fc2\u3092\u6301\u3063\u3066\u3044\u308b\u3060\u3051\u3067\u306f\u3042\u308a\u307e\u305b\u3093 \u5b8c\u74a7 \u4f5c\u3089\u308c\u305f6\u3064\u306e\u756a\u53f7\u3001 [20] \u3057\u304b\u3057\u3001\u5f7c\u306e\u8a69\u7684\u306a\u4e3b\u306a\u4f5c\u54c1\u3067\u3082\u3001 \u5341\u5b57\u67b6\u306e\u81ea\u7531\u306a\u8cde\u8cdb\u3001 [21] \u306e\u7dcf\u5efa\u7269 \u5b8c\u74a7 28\u30a2\u30e9\u30a4\u30f3\u30c9\u3002\u3053\u306e\u4f5c\u54c1\u306f28\u306e\u8a69\u3067\u69cb\u6210\u3055\u308c\u3066\u3044\u307e\u3059 \uff08\u30b7\u30a2\u30f3\u306e\u6bd4ur\u7684\uff09 \u6563\u6587\u5ba3\u8a00\u3068\u6563\u6587\u306e\u8a00\u3044\u63db\u3048\u304c\u6563\u6587\u306b\u6dfb\u4ed8\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u56f3\u306e\u8a69\u81ea\u4f53\u306f\u3001\u8a69\u306e\u4e2d\u306e\u540c\u3058\u6570\u306e\u6587\u5b57\u306e\u30d8\u30ad\u30b5\u30e1\u30fc\u30bf\u30fc\u3067\u66f8\u304b\u308c\u3066\u304a\u308a\u3001\u8868\u73fe\u305b\u305a\u306b\u539f\u7a3f\u306b\u66f8\u304b\u308c\u3066\u3044\u308b\u305f\u3081\u3001\u30e1\u30c8\u30ea\u30c3\u30af\u30c6\u30ad\u30b9\u30c8\u304c\u9577\u65b9\u5f62\u306e\u30d6\u30ed\u30c3\u30af\u3068\u3057\u3066\u8868\u793a\u3055\u308c\u307e\u3059\u3002\u3053\u306e\u30d6\u30ed\u30c3\u30af\u5185\u3067\u3001\u500b\u3005\u306e\u6587\u5b57\u304c\u8272\u3068\u5468\u56f2\u306e\u89b3\u70b9\u304b\u3089\u5f37\u8abf\u8868\u793a\u3055\u308c\u3001\u305d\u308c\u304c\u518d\u3073\u65b0\u3057\u3044\u30c6\u30ad\u30b9\u30c8\u3092\u5f62\u6210\u3059\u308b\u305f\u3081\u3001 intext\u306b\u5411\u304b\u3063\u3066 \u305d\u308c\u3089\u3092\u307e\u3068\u3081\u3066\u304f\u3060\u3055\u3044\u3002\u3053\u308c\u3089\u306e\u6570\u5b57\u306e28\u65e5\u3068\u6700\u5f8c\u306e\u6563\u6587\u5ba3\u8a00\u3067\u306f\u3001Hrabanus\u306f28\u756a\u306e\u9078\u629e\u306e\u7406\u7531\u3082\u6307\u6458\u3057\u3066\u3044\u307e\u3059\u3002 [22] \u300c\u305d\u308c\u306f\u3059\u3079\u3066\u306e\u672c\u306b28\u306e\u6563\u6587\u306e\u6570\u5b57\u3092\u542b\u3093\u3067\u3044\u307e\u3059\uff08…\uff09\uff1a100\u5468\u5e74\u306e\u515a\u306e\u6570\u306f\u5b8c\u5168\u306b\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u30ab\u30f3\u30bf\u30f4\u30a3\u30c3\u30c8\u306e\u5b8c\u74a7\u3055\u3092\u30ab\u30f3\u30bf\u30f4\u30a3\u30c3\u30c8\u3067\u5f62\u6210\u3059\u308b\u4f5c\u696d\u4ed5\u4e0a\u3052\u306b\u3088\u308b\u3068\u3002\u300d \u300c\u3057\u304b\u3057\u3001\u305d\u308c\u306f\u305d\u306e\u5f8c\u306e\u6563\u6587\uff08…\uff09\u3092\u6301\u3064\u672c28\u30e1\u30fc\u30c8\u30eb\u306e\u6570\u5b57\u3092\u542b\u3093\u3067\u3044\u307e\u3059\uff08…\uff09\uff1a\u3053\u306e\u6570\u306f\u305d\u306e\u90e8\u5206\u3067\u6e80\u305f\u3055\u308c\u3066\u3044\u308b100\u306e\u9818\u57df\u306b\u3042\u308a\u307e\u3059\u3002\u3060\u304b\u3089\u3001\u79c1\u306f\u3053\u306e\u4f5c\u54c1\u306e\u3053\u306e\u91cf\u3092\u5b8c\u6210\u3055\u305b\u305f\u3044\u3068\u601d\u3063\u3066\u3044\u307e\u3059\u3002 Burkhard Taeger\uff081972\uff09\u304c\u73fe\u4ee3\u3067\u767a\u898b\u3057\u305f\u3088\u3046\u306b\u3001 [23] \u6570\u306e\u7b97\u8853\u7684\u7406\u89e3\u3082\u3001\u4f5c\u696d\u306e\u6b63\u5f0f\u306a\u69cb\u9020\u306b\u3055\u3089\u306b\u6df1\u304f\u4ecb\u5165\u3057\u307e\u3059\u3002 28\u306e\u8a69\u304c\u8a69\u3042\u305f\u308a\u306e\u6587\u5b57\u306e\u6570\u306b\u5f93\u3063\u3066\u5206\u5272\u3055\u308c\u3066\u3044\u308b\u5834\u5408\u30011\u30012\u30014\u30017\u300114\u306e\u8a69\u306e\u30b0\u30eb\u30fc\u30d7\u304c\u3042\u308b\u305f\u3081\u3001\u4f5c\u54c1\u306e\u5185\u90e8\u69cb\u9020\u3082 \u5b8c\u5168 \u5f7c\u3089\u306b\u3088\u308b28\u306e\u6210\u5c31 \u90e8\u54c1 \u53cd\u5c04\u3002 \u6570\u5b57\u306e\u6839\u5e95\u306b\u3042\u308b\u7406\u89e3\u306e\u8a69\u7684\u306a\u9069\u5fdc\u306e\u8a3c\u62e0\u306f\u3001\u5f8c\u671f\u4e2d\u4e16\u306b\u3082\u898b\u3089\u308c\u307e\u3059\u3002 [24] \u307e\u305f\u3001\u901a\u5e38\u3001\u4f5c\u54c1\u3092\u69cb\u7bc9\u3059\u308b\u305f\u3081\u306b\u8aac\u660e\u7684\u306a\u6dfb\u52a0\u7269\u306a\u3057\u3067\u4ef2\u826f\u304f\u3057\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\u8996\u899a\u82b8\u8853\u3067\u306f\u3001\u30a2\u30c3\u30b7\u30b8\u306e\u4e0a\u90e8\u5927\u8056\u5802\u306e\u8056\u30d5\u30e9\u30f3\u30b7\u30b9\u30b3\u306e\u4eba\u751f\u306b\u3064\u3044\u3066\u306e\u30b8\u30e7\u30c3\u30c8\u306e28\u306e\u30d5\u30ec\u30b9\u30b3\u753b\u306f\u3001\u5f7c\u306e\u4eba\u751f\u306e\u30ad\u30ea\u30b9\u30c8\u6559\u306e\u8056\u306a\u308b\u5b8c\u5168\u6027\u3068\u985e\u4f3c\u6027\u3092\u5c01\u5370\u3057\u305f\u3044\u3068\u8003\u3048\u3066\u3044\u307e\u3059\u3002 [25] \u30b9\u30bf\u30f3\u30ea\u30fc\u30fbJ\u30fb\u30d9\u30b6\u30c1\u30ab\uff1a \u5b8c\u74a7\u306a\u6570\u5b57 – \u66f4\u65b0\u3002 \u306e\uff1a \u6570\u5b66\u6559\u5e2b\u3002 \u30d0\u30f3\u30c974\u30011981\u3001S\u3002460\u2013463\u3002 \u30b9\u30bf\u30f3\u30ea\u30fc\u30fbJ\u30fb\u30d9\u30ba\u30b7\u30e5\u30ab\u3001\u30de\u30fc\u30ac\u30ec\u30c3\u30c8\u30fbJ\u30fb\u30b1\u30cb\u30fc\uff1a \u5b8c\u5168\u306a\u6570\u5b57\u3067\u3055\u3048\uff1a\uff08\u66f4\u65b0\uff09\u00b2\u3002 \u306e\uff1a \u6570\u5b66\u6559\u5e2b\u3002 \u30d0\u30f3\u30c990\u30011997\u3001S\u3002628\u2013633\u3002 \u30dd\u30fc\u30eb\u30fb\u30a8\u30eb\u30c9\u30b9\u3001\u30b8\u30e7\u30f3\u30fb\u30b5\u30fc\u30cb\u30fc\uff1a \u6570\u5b57\u306e\u7406\u8ad6\u306e\u30c8\u30d4\u30c3\u30af \uff08= \u6570\u5b66\u306e\u5b66\u90e8\u30c6\u30ad\u30b9\u30c8 \uff09\u3002\u7b2c2\u7248\u200b\u200b\u3002 Springer\u3001New York 2003\u3001ISBN 0-387-95320-5\uff08\u82f1\u8a9e\u3001\u30cf\u30f3\u30ac\u30ea\u30fc\u8a9e\uff1a Number Theory\u304b\u3089\u9078\u629e\u3055\u308c\u305f\u7ae0 \u3002 Barry Guiduli\u306b\u3088\u308b\u7ffb\u8a33\uff09\u3002 \u30aa\u30c3\u30c8\u30fc\u30fb\u30b0\u30ea\u30e5\u30f3\uff1a \u5947\u5999\u306a\u5b8c\u74a7\u306a\u6570\u5b57\u306b\u3064\u3044\u3066 \u3002\u306e\uff1a \u6570\u5b66\u96d1\u8a8c \u3002 \u30d0\u30f3\u30c9 55 \u3001 \u3044\u3044\u3048\u3002 3 \u30011952\u5e74\u3001 S. 353\u2013354 \u3001doi\uff1a 10.1007\/BF01181133 \u3002 D. R.\u30d2\u30fc\u30b9\u30d6\u30e9\u30a6\u30f3\uff1a \u5947\u5999\u306a\u5b8c\u74a7\u306a\u6570\u5b57 \u3002\u306e\uff1a \u30b1\u30f3\u30d6\u30ea\u30c3\u30b8\u54f2\u5b66\u5354\u4f1a\u306e\u6570\u5b66\u7684\u624b\u7d9a\u304d \u3002 \u30d0\u30f3\u30c9 115 \u3001 \u3044\u3044\u3048\u3002 2 \u30011994\u5e74\u3001 S. 191\u2013196 \u3001doi\uff1a 10.1017\/s0305004100072030 \uff08 \u5168\u6587 [PDF; 117 KB ; 2017\u5e746\u670816\u65e5\u306b\u30a2\u30af\u30bb\u30b9]\uff09\u3002 ullrichk\u00fcnel\uff1a \u5947\u5999\u306a\u5b8c\u5168\u306a\u6570\u5b57\u306e\u5b58\u5728\u306b\u5fc5\u8981\u306a\u6761\u4ef6\u3092\u5f15\u304d\u7de0\u3081\u308b\u3002 \u306e\uff1a \u6570\u5b66\u96d1\u8a8c\u3002 \u30d0\u30f3\u30c952\u3001nr\u3002 1\u30011950\u3001S\u3002202-211\u3001 doi\uff1a10.1007\/bf02230691 \u3002 J\u00f3zsefS\u00e1ndor\u3001Dragoslav S.Mitrinovi\u0107\u3001Borislav Crstiica\uff1a \u6570\u5b57\u7406\u8ad6\u306e\u30cf\u30f3\u30c9\u30d6\u30c3\u30af\u3002\u79c1 \u3002 Springs Publisher\u3001Drogue 146\u3001ISBN 978-1-4020-4255- S\u00e1ndorJ\u00f3zsef\u3001Borislav Crstici\uff1a \u6570\u5b57\u7406\u8ad6\u306e\u30cf\u30f3\u30c9\u30d6\u30c3\u30af\u3002 ii \u3002 Kluwer Academic Publishers\u3001Dordrecht\/Boston\/London 2004\u3001ISBN 1-4020-2546-7\u3002 wac\u0142awsierpi\u0144ski\uff1a \u6570\u5b57\u306e\u57fa\u672c\u7406\u8ad6 \uff08= \u30ce\u30fc\u30b9\u30db\u30e9\u30f3\u30c9\u6570\u5b66\u30e9\u30a4\u30d6\u30e9\u30ea \u3002 \u30d0\u30f3\u30c9 \u6700\u521d\u306b30 \uff09\u3002 2.\u6539\u8a02\u304a\u3088\u3073\u62e1\u5f35\u7248\u3002\u30ce\u30fc\u30b9\u30db\u30e9\u30f3\u30c9\uff08\u3092\u542b\u3080\uff09\u3001\u30a2\u30e0\u30b9\u30c6\u30eb\u30c0\u30e0\uff08\u304a\u3088\u3073\u3002\uff091988\u3001ISBN 0-444-86662-0\u3002 \u2191 \u65e2\u77e5\u306e\u30e1\u30eb\u30bb\u30f3\u30cc\u30d7\u30e9\u30a4\u30e0\u30ca\u30f3\u30d0\u30fc\u306e\u30ea\u30b9\u30c8-Primenet\u3002 \u306e\uff1a mersenne.org\u3002 2019\u5e741\u67082\u65e5\u306b\u30a2\u30af\u30bb\u30b9 \u3002 \u2191 a b Sierpi\u0144ski\uff1a \u6570\u5b57\u306e\u57fa\u672c\u7406\u8ad6 \u3002 S. 182 ff \u3002 \u2191 Alexander-Crstici\uff1a \u6570\u5b57\u7406\u8ad6\u306e\u30cf\u30f3\u30c9\u30d6\u30c3\u30af\u3002 ii \u3002 S. 23 ff \u3002 \u2191 s\u00e1ndor-mitrinovi\u0107-crstici\uff1a \u6570\u5b57\u7406\u8ad6\u306e\u30cf\u30f3\u30c9\u30d6\u30c3\u30af\u3002\u79c1 \u3002 S. 100 ff \u3002 \u2191 \u30d1\u30b9\u30ab\u30eb\u30fb\u30aa\u30b7\u30a7\u30e0\u3001\u30de\u30a4\u30b1\u30eb\u30fb\u30e9\u30aa\uff1a \u5947\u5999\u306a\u5b8c\u74a7\u306a\u6570\u5b57\u306f10\u3092\u8d85\u3048\u3066\u3044\u307e\u3059 1500 \u3002\u306e\uff1a \u8a08\u7b97\u306e\u6570\u5b66 \u3002 \u30d0\u30f3\u30c9 81 \u3001 \u3044\u3044\u3048\u3002 279 \u30011\u3002Januar2012\u3001ISSN 0025-5718 \u3001 S. 1869\u20131877 \u3001doi\uff1a 10.1090\/s0025-5718-2012-02563-4 \uff08 ams.org [2017\u5e743\u67085\u65e5\u306b\u30a2\u30af\u30bb\u30b9]\uff09\u3002 \u2191 Judy A. Holdener\uff1a \u5947\u5999\u306a\u5b8c\u74a7\u306a\u6570\u5b57\u306e\u5f62\u306e\u30bf\u30c3\u30c1\u30e3\u30fc\u30c9\u306e\u5b9a\u7406\u3002 \u306e\uff1a \u5348\u524d\u3002\u7b97\u6570\u3002\u6708\u66dc\u65e5 109\u3001No\u30027\u3001661\u2013663\uff082002\uff09\u3002 \u2191 \u3057\u305f\u304c\u3063\u3066\u3001\u6574\u6570\u5e2b\u56e3\u3092\u5099\u3048\u305f\u30ec\u30e0\u30ca\u30f3\u30c81\u309212\u307e\u305f\u306f\u6b8b\u308a9\u3092\u53d6\u5f97\u3057\u307e\u3059\u3002 \u2191 a b c d \u305d\u3046\u3067\u3059 f Paolo Ribenboim\uff1a \u7d20\u6570\u306e\u4e16\u754c – \u79d8\u5bc6\u3068\u8a18\u9332 \u3002\u7b2c2\u7248\u200b\u200b\u3002 Springer-Verlag\u30012011\u3001ISBN 978-3-642-18079-8\u3001 S. 86\u201387 \u3002 \u2191 Alexander-Crstici\uff1a \u6570\u5b57\u7406\u8ad6\u306e\u30cf\u30f3\u30c9\u30d6\u30c3\u30af\u3002 ii \u3002 S. 36\u201337 \u3002 \u2191 s\u00e1ndor-mitrinovi\u0107-crstici\uff1a \u6570\u5b57\u7406\u8ad6\u306e\u30cf\u30f3\u30c9\u30d6\u30c3\u30af\u3002\u79c1 \u3002 S. 109\u2013110 \u3002 \u2191 \u30dc\u30a8\u30c6\u30a3\u30a6\u30b9\uff1a \u6a5f\u95a2\u306e\u7b97\u88532\u518a\u306e\u672c\u3002 Gottfried Friedleich\uff08\u4e00\u7dd2\u306b\u7de8\u96c6 \u97f3\u697d\u306e\u5236\u5ea6 \uff09\u3001Leipzig 1867\u3001Nachdr\u3002MinervaGmbh\u3001Frankfurt\/Main 1966;\u4e2d\u4e16\u306e\u30ec\u30bb\u30d7\u30b7\u30e7\u30f3\u306b\u3064\u3044\u3066\u306f\u3001Pearl Kibre\uff1a \u30d1\u30ea\u306e13\u4e16\u7d00\u306e\u5927\u5b66\u74b0\u5883\u306e\u7b97\u8853\u3068\u56db\u5143\u6570\u306e\u30dc\u30a8\u30b7\u30a2\u30f3\u3002 In\uff1aMichael Masi\uff08\u7de8\uff09\uff1a \u30dc\u30a8\u30c6\u30a3\u30a6\u30b9\u3068\u30ea\u30d9\u30e9\u30eb\u30a2\u30fc\u30c4\uff1a\u30a8\u30c3\u30bb\u30a4\u306e\u30b3\u30ec\u30af\u30b7\u30e7\u30f3\u3002 Verlag Peter Lang\u3001Bern \/ Frankfurt \/ Main \/ Las Vegas 1981\uff08= \u6587\u5b66\u3068\u8a00\u8a9e\u5b66\u306e\u30e6\u30bf\u7814\u7a76\u3001 18\uff09\u3001S\u300267\u201380;\u30de\u30a4\u30b1\u30eb\u307e\u3060\uff1a \u30dc\u30a8\u30c6\u30a3\u30a6\u30b9\u306e\u5f71\u97ff \u7b97\u8853\u306e \u5f8c\u671f\u4e2d\u4e16\u306e\u6570\u5b66\u306b\u3064\u3044\u3066\u3002 \u540c\u4e0a\u3001pp\u300281\u201395\u3002 \u2191 Nikomachos von Gerasa: \u7b97\u8853\u7d39\u4ecb\u3002 \u30ea\u30c1\u30e3\u30fc\u30c9\u30fb\u30db\u30fc\u30b7\u30a7\u7de8\u3001\u30c6\u30a6\u30d6\u30ca\u30fc\u30fb\u30f4\u30a7\u30eb\u30e9\u30b0\u3001\u30e9\u30a4\u30d7\u30c4\u30a3\u30d21866;\u30d3\u30b6\u30f3\u30c1\u30f3\u7b97\u8853\u306e\u5b8c\u5168\u306a\u6570\u5b57\u306e\u4f1d\u7d71\u306b\u3064\u3044\u3066\u306f\u3001Nicole Zeegers-Vander\u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044\u3002 11\u4e16\u7d00\u306e\u533f\u540d\u306e\u30ab\u30c9\u30ea\u30d3\u30a6\u30e0\u306e\u7b97\u8853\u3002 \u306e\uff1a \u53e4\u5178\u7684\u306a\u53e4\u4ee3\u3002 32\uff081963\uff09\u3001S\u3002129\u2013161\u3001bes\u3002 S. 144 f\u3002 \u2191 \u30dc\u30a8\u30c6\u30a3\u30a6\u30b9\uff1a \u6a5f\u95a2\u306e\u7b97\u8853\u3002 lib\u3002i\u3001cap\u3002 19\u201320\u3001ed\u3002Friedlein1867\u3001pp\u300239\u201345\u3002\u30e9\u30c6\u30f3\u8a9e\u306e\u4f1d\u7d71\u306b\u304a\u3051\u308b\u30dc\u30a8\u30c6\u30a3\u30a6\u30b9\u306e\u8868\u73fe\u3068\u3057\u3066\u3001Martianus capella\uff1a\u3082\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044\u3002 nvptiis phalology and Mercvrii\u3002 VII\u3001753\u3001\u7de8James Willis\u3001Teubner Verlag\u3001Leipzig 1983;\u30de\u30af\u30ed\u30d3\u30a6\u30b9\uff1a \u30b7\u30d4\u30aa\u306e\u5922\u306b\u95a2\u3059\u308b\u89e3\u8aac\u3002 I\u3001vi\u300112\u3001ed\u3002 Jakob Willis\u3001Teubner Verlag\u3001Leipzig 1963;\u3068cassiodor\uff1a \u82b8\u8853\u3068\u5206\u91ce\u306e\u30ea\u30d9\u30e9\u30eb\u306a\u624b\u7d19\u3002 VII\u3001PL 70.1206\u3002\u3053\u308c\u3089\u306f\u540c\u3058\u7b97\u8853\u7684\u7406\u89e3\u3092\u793a\u3057\u307e\u3059\u304c\u3001\u8a73\u7d30\u306b\u306f\u3042\u307e\u308a\u5b9f\u884c\u3057\u307e\u305b\u3093\u3002\u306e\u305f\u3081\u306e\u5225\u306e\u6b63\u5f53\u5316 \u5b8c\u74a7 Vitruvius\u306f6\u3064\u306e\u756a\u53f7\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002 \u5efa\u7bc9\u5b66\u3001\u5efa\u7bc9\u7269\u3001\u5efa\u7bc9\u69d8\u5f0f\u3002 III\u3001I\u30016\uff08\u7de8\u96c6\u3001\u304a\u3088\u3073Curt Fensterbusch\u3001Scientific Book Society\u3001Darmstadt 1964\u306b\u3088\u308b\u7ffb\u8a33\uff09\u3002 \u2191 Isidor von Sevilla\uff1a \u8a9e\u6e90\u3002 vii\u3001v\u3002 9\u201311\u3001\u7de8Wallace M. Lindsay\u3001Clarendon Press\u3001\u30e9\u30a4\u30d7\u30c4\u30a3\u30d21911\u3002 \u2191 \u30b9\u30bf\u30f3\u30ea\u30fc\u30fbJ\u30fb\u30d9\u30b6\u30c1\u30ab\uff1a \u5b8c\u74a7\u306a\u6570\u5b57 – \u66f4\u65b0\u3002 \u306e\uff1a \u6570\u5b66\u6559\u5e2b\u3002 74\uff081981\uff09\u3001pp\u3002460\u2013463\u3002 1997\u5e74\u307e\u3067\u4ed6\u306e\u5b8c\u74a7\u306a\u6570\u5b57\u306e\u767a\u898b\u306e\u6b74\u53f2\u306b\u3064\u3044\u3066\uff1a\u30b9\u30bf\u30f3\u30ea\u30fcJ.\u30d9\u30ba\u30b7\u30e5\u30ab\u3001\u30de\u30fc\u30ac\u30ec\u30c3\u30c8J.\u30b1\u30cb\u30fc\uff1a \u5b8c\u5168\u306a\u6570\u5b57\u3067\u3055\u3048\uff1a\uff08\u66f4\u65b0\uff09\u00b2\u3002 \u306e\uff1a \u6570\u5b66\u6559\u5e2b\u3002 90\uff081997\uff09\u3001S\u3002628\u2013633\u3002 \u2191 \u30cf\u30a4\u30f3\u30c4\u30fb\u30de\u30a4\u30e4\u30fc\uff1a \u4e2d\u4e16\u306e\u6570\u306eall\u8a71\uff1a\u65b9\u6cd5\u3068\u4f7f\u7528\u3002 Wilhelm Finck Verlag\u3001Munich 1975\uff08= \u30df\u30e5\u30f3\u30b9\u30bf\u30fc\u4e2d\u4e16\u306e\u8457\u4f5c25\u3002 \uff09pp\u300230\u201335; Heinz Meyer \/ Horst Suntrup\uff08ed\u3002\uff09\uff1a \u4e2d\u4e16\u6570\u306e\u8f9e\u66f8\u3002 Wilhelm Finck Verlag\u3001Munich 1987\uff08= MMS 56\u3002 \uff09Art\u30026\u3001sp\u3002442\u2013479\u3002 \u2191 \u30aa\u30fc\u30ac\u30b9\u30c6\u30a3\u30f3\uff1a \u5275\u4e16\u8a18\u306e\u6587\u5b57\u901a\u308a\u3002 IV\u30011\u20137\u3001Cel 28.1\uff081894\uff09\u3001pp\u300293-103;\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044 \u4e09\u4f4d\u4e00\u4f53\u306e\u3002 4\u30014-6\u3001CCSL 50\uff081968\uff09\u3001S\u3002169-175\u3002 \u2191 \u4e2d\u4e16\u6587\u732e\u306e\u69cb\u9020\u306b\u304a\u3051\u308b\u6570\u5b57\u3068\u6570\u5024\u95a2\u4fc2\u3092\u89e3\u91c8\u3059\u308b\u65b9\u6cd5\u8ad6\u7684\u8981\u4ef6\u306b\u3064\u3044\u3066\u306f\u3001Ernst Hellgardt\u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044\u3002 \u4e2d\u4e16\u6587\u732e\u306b\u304a\u3051\u308b\u8c61\u5fb4\u7684\u304a\u3088\u3073\u6b63\u5f0f\u306a\u7f8e\u7684\u6570\u306e\u554f\u984c\u3002 C. H.\u30d9\u30c3\u30af\u3001\u30df\u30e5\u30f3\u30d8\u30f31973\uff08= \u30df\u30e5\u30f3\u30d8\u30f3\u306e\u30c6\u30ad\u30b9\u30c8\u3068\u7814\u7a76\u3002 \u7b2c45\u5dfb\uff09\u3001ISBN 978-3-4060-2845-8; otfried lieberknecht\uff1a Allegoresis and Phology\uff1aDantes Commedia\u306e\u8907\u6570\u306e\u30d6\u30ea\u30fc\u30d5\u30a3\u30f3\u30b0\u306e\u554f\u984c\u306b\u95a2\u3059\u308b\u8003\u5bdf\u3002 Franz Steiner Verlag\u3001Stuttgart 1999\uff08= \u30c6\u30ad\u30b9\u30c8\u3068\u30b3\u30f3\u30c6\u30ad\u30b9\u30c8\u300114\u3002 \uff09S\u3002133 ff\u3002 \uff08 \u30aa\u30f3\u30e9\u30a4\u30f3\u30d0\u30fc\u30b8\u30e7\u30f3\u306f\u3053\u3061\u3089\u3002 \uff09\uff09 \u2191 \u30a2\u30eb\u30af\u30a4\u30f3\uff1a Epistola 309\uff08AD Gundradam\uff09\u3002 In \uff1a\uff08\u30af\u30a9\u30fc\u30c8\uff094\uff1a Karolini Aevi\uff082\uff09\u3002 herausgegeben von ernstd\u00fcmmleru\u3002 a\u3002\u30d9\u30eb\u30ea\u30f3\u30011895\u5e74\u3001S\u3002473-478\uff08Monument Germany Histilica\u3001 \u30c7\u30b8\u30bf\u30eb\u5316 \uff09Paul Klopsch\uff08\u7de8\uff09\u304b\u3089\u5f15\u7528\u3055\u308c\u305f\u7ffb\u8a33\uff1a \u4e2d\u4e16\u306e\u30e9\u30c6\u30f3\u8a69\u3002 Reclam-verlag\u3001Stuttgart 1985\uff08= Universal-Bibliotek\u30af\u30ec\u30fc\u30e0\u30018088\u3002 \uff09\u3002 \u2191 \u30ab\u30eb\u30df\u30ca\u3002 In\uff1a\u8a69\u4eba\u4e2d\u4e162\uff1a \u8a69\u4eba\u30a8\u30f4\u30a3\u30fb\u30ab\u30ed\u30ea\u30fc\u30cb\uff082\uff09\u3002 Herausgegeben von ErnstD\u00fcmmler\u3002\u30d9\u30eb\u30ea\u30f31884\u3001S\u3002154-258\uff08Monument Historica; \u30c7\u30b8\u30bf\u30eb\u5316 \uff09\u3002\u305f\u3068\u3048\u3070\u3001\u30c1\u30e3\u30fc\u30e0\u3002 xviii\u3001vv\u3002 55\u201360\u30de\u30a4\u30f3\u30c4\u5927\u53f8\u6559\u306e\u30aa\u30c8\u30ac\u30fc\u306b\u300166\u7bc0\u306e\u6570\u306f\u3001\u53d7\u4fe1\u8005\u304c\u300c\u5b8c\u5168\u306b\u7fd2\u6163\u3068\u5b8c\u74a7\u306a\u7d33\u58eb\u306b\u5c5e\u3059\u308b\u53ec\u4f7f\u300d\u3068\u3044\u3046\u9858\u3044\u3067\u6b63\u5f53\u5316\u3055\u308c\u307e\u3059\u3002 \uff08\u5b8c\u74a7\u306a\u884c\u52d5\u3068 \/\u5974\u96b7\u306b\u5f93\u3063\u305f\u5b8c\u74a7\u306a\u6240\u6709\u8005\uff09 \u591a\u5206\u3002 \u2191 Mignes\u306e\u5f8c\u306b\u3053\u3053\u3067\u5f15\u7528\u3055\u308c\u3066\u3044\u307e\u3059\u3002 \u8056\u5341\u5b57\u67b6\u306e\u8cde\u8cdb\u3002 PL 107\u3001133\u2013294\u3001Michel Perrin\u306b\u3088\u308b\u65b0\u3057\u3044\u30af\u30ea\u30c6\u30a3\u30ab\u30eb\u30a8\u30c7\u30a3\u30b7\u30e7\u30f3\u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044\uff1a \u8056\u5341\u5b57\u67b6\u306b\u656c\u610f\u3092\u8868\u3057\u3066\u3002 CCCM 100\uff081997\uff09\u304a\u3088\u3073\u30ab\u30fc\u30c8\u30db\u30eb\u30bf\u30fc\u306e\u30d5\u30a1\u30af\u30b7\u30df\u30ea\u7248\uff08\u7de8\uff09\uff1a Laudibus Sanctae Crucis\u3002\u30aa\u30fc\u30b9\u30c8\u30ea\u30a2\u56fd\u7acb\u56f3\u66f8\u9928\u306eCodex vindobonensis 652\u306e\u5143\u306e\u5f62\u5f0f\u306e\u5b8c\u5168\u306a\u30d5\u30a1\u30af\u30b7\u30df\u30ea\u7248\u3002 \u30a2\u30ab\u30c7\u30df\u30c3\u30af\u5370\u5237\u3068\u51fa\u7248\u793e\u3001Graz 1973\uff08= CODICES\u30e9\u30a4\u30d6\u30e9\u30ea\u300133\u3002 \uff09\u3002 \u2191 Hrabanus Maurus\uff1a \u8056\u5341\u5b57\u67b6\u306e\u8cde\u8cdb\u3002 Lib\u3002I\u3001figura xxviii\u3001pl 107,264; 6\u3064\u306e\u9069\u7528\u306e\u4f8b\u3068\u3057\u3066\u3001\u5b8c\u74a7\u306a\u6570\u5b57\u3068\u3057\u3066\u3001Figura XXIII\u304a\u3088\u3073 \u56f3\u306e\u5ba3\u8a00 PL 107\u3001239\u2013242\u3002 \u2191 \u30d0\u30fc\u30af\u30cf\u30eb\u30c8\u30c6\u30fc\u30ac\u30fc\uff1a \u6570\u5b57\u306e\u8c61\u5fb4\u6027\u3001Hraban\u3001Hincmar – \u304a\u3088\u3073\u300cHeliand\u300d\u3067\uff1f H. C.\u30d9\u30c3\u30af\u3001\u30df\u30e5\u30f3\u30d8\u30f31972\uff08= \u30df\u30e5\u30f3\u30d8\u30f3\u306e\u30c6\u30ad\u30b9\u30c8\u3068\u7814\u7a76\u300130\u3002 \uff09\u3002 \u2191 Dante Alighieri\u306b\u3064\u3044\u3066\u306f\u3001Otfried Lieberknecht\u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044\uff1a \u7b97\u8853\u3001\u7cbe\u795e\u7684\u306a\u89e3\u91c8\u3001\u4e2d\u4e16\u306e\u6587\u5b66\u6570\u306e\u69cb\u6210\u306b\u304a\u3051\u308b\u300c\u5b8c\u74a7\u306a\u6570\u300d\u3002 \u8b1b\u7fa9\u3001\u30ab\u30a4\u30b6\u30fc\u30b9\u30e9\u30a6\u30bf\u30fc\u5927\u5b66\u3001\u7279\u5225\u30a4\u30d9\u30f3\u30c8 \u6570\u5b66\u306e\u6b74\u53f2\u3001 1998\u5e742\u670818\u65e5\u3002 ders\u3002\uff1a Dante\u306e\u6b74\u53f2\u7684\u306a\u7b97\u8853\uff1aHell 28\u306e\u300c\u96c6\u7d04\u306e\u4e00\u90e8\u306b\u5b8c\u5168\u306b\u5fdc\u3058\u305f\u6570\u5b57\u300d\u3068\u3057\u30666\u306828\u306e\u6570\u5b57\u3002 Vortrag\u3001\u7b2c32\u56de\u4e2d\u4e16\u7814\u7a76\u306b\u95a2\u3059\u308b\u56fd\u969b\u4f1a\u8b70\u3001\u897f\u30df\u30b7\u30ac\u30f3\u5927\u5b66\u3001\u30ab\u30e9\u30de\u30ba\u30fc\u30011997\u5e74\u3002 \u2191 Fritz Tschirch\u3082\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044\uff1a \u6587\u5b66\u7684\u306a\u69cb\u9020\u306e\u5c0f\u5c4b\u306e\u79d8\u5bc6\u3002\u4e2d\u4e16\u306e\u30b7\u30fc\u30eb\u306e\u30b7\u30f3\u30dc\u30eb\u304c\u6c7a\u5b9a\u3055\u308c\u305f\u7bc4\u56f2\u304b\u3089\u3002 In\uff1aders\u3002\uff1a \u30b9\u30e2\u30fc\u30eb\u30ba\u3002\u30c9\u30a4\u30c4\u306e\u7814\u7a76\u3068\u795e\u5b66\u306e\u56fd\u5883\u96e8\u304b\u3089\u306e\u7814\u7a76\u3002 Erich Schmidt Verlag\u3001Berlin 1966\u3001pp\u3002212\u2013225\u3001\u3053\u3053\u3067213\u756a\u53f728\u3002 (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/14529#breadcrumbitem","name":"\u30d1\u30fc\u30d5\u30a7\u30af\u30c8\u30ca\u30f3\u30d0\u30fc – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2"}}]}]