[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/19438#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/19438","headline":"Fermatscher Prime FAG -Wikipedia","name":"Fermatscher Prime FAG -Wikipedia","description":"before-content-x4 Fermatsch Prime FAG \u5c0f\u3055\u306a\u30d5\u30a1\u30fc\u30de\u30c3\u30c1\u30a7\u30f3\u6587\u306b\u57fa\u3065\u3044\u305f\u4e3b\u8981\u306a\u30c6\u30b9\u30c8\u3067\u3059\u3002\u7d20\u6570\u3068\u8907\u5408\u756a\u53f7\u3092\u533a\u5225\u3059\u308b\u306e\u306b\u5f79\u7acb\u3061\u307e\u3059\u3002 after-content-x4 Felmatsch Prime Natural Test\u306f\u3001\u5c0f\u3055\u306aFermatschen\u6587\u306b\u57fa\u3065\u3044\u3066\u3044\u307e\u3059\u3002 \u3059\u3079\u3066\u306e\u7d20\u6570\u7528 p {displaystyle p} \u305d\u3057\u3066\u3001\u3059\u3079\u3066\u306e\u975e\u9694\u96e2\u3055\u308c\u305f\u81ea\u7136\u6570 a {displaystyle a} \u6b21\u306e\u4e00\u81f4\u304c\u6e80\u305f\u3055\u308c\u3066\u3044\u307e\u3059\u3002 after-content-x4","datePublished":"2023-09-11","dateModified":"2023-09-11","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\/81eac1e205430d1f40810df36a0edffdc367af36","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/81eac1e205430d1f40810df36a0edffdc367af36","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/19438","wordCount":3071,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4 Fermatsch Prime FAG \u5c0f\u3055\u306a\u30d5\u30a1\u30fc\u30de\u30c3\u30c1\u30a7\u30f3\u6587\u306b\u57fa\u3065\u3044\u305f\u4e3b\u8981\u306a\u30c6\u30b9\u30c8\u3067\u3059\u3002\u7d20\u6570\u3068\u8907\u5408\u756a\u53f7\u3092\u533a\u5225\u3059\u308b\u306e\u306b\u5f79\u7acb\u3061\u307e\u3059\u3002        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4Felmatsch Prime Natural Test\u306f\u3001\u5c0f\u3055\u306aFermatschen\u6587\u306b\u57fa\u3065\u3044\u3066\u3044\u307e\u3059\u3002 \u3059\u3079\u3066\u306e\u7d20\u6570\u7528 p {displaystyle p} \u305d\u3057\u3066\u3001\u3059\u3079\u3066\u306e\u975e\u9694\u96e2\u3055\u308c\u305f\u81ea\u7136\u6570 a {displaystyle a} \u6b21\u306e\u4e00\u81f4\u304c\u6e80\u305f\u3055\u308c\u3066\u3044\u307e\u3059\u3002        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4ap\u22121\u559c\u3093\u3067 \u521d\u3081 \u306b\u5bfe\u3057\u3066 p {displaystyle a^{p-1} equiv 1mod p} \u3002 \u3053\u306e\u72b6\u614b\u3092\u9006\u8ee2\u3055\u305b\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u81ea\u7136\u6570\u3092\u69cb\u6210\u3057\u3066\u3044\u308b\u304b\u3069\u3046\u304b\u3092\u30c6\u30b9\u30c8\u3067\u304d\u307e\u3059\u3002\u305d\u308c\u306f…\u3067\u3059\u304b a n\u22121 –  \u521d\u3081 {displaystyle a^{n-1} -1} 1\u3064\u3082 n {displaystyle n} \u30d9\u30fc\u30b9\u30d9\u30fc\u30b9        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4a {displaystyle a} \u901a\u308a\u3067\u306f\u3042\u308a\u307e\u305b\u3093 n {displaystyle n} \u5206\u88c2\u53ef\u80fd\u306a\u306e\u3067\u3001\u305d\u3046\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059 n {displaystyle n} \u30d7\u30e9\u30a4\u30e0\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u305f\u3068\u3048\u3070\u3001\u51fa\u3066\u884c\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059 2 9\u22121= 2 8= 256 = 28 de 9 + 4 \u559c\u3093\u3067 4 \u306b\u5bfe\u3057\u3066 9 {displaystyle 2^{9-1} = 2^{8} = 256 = 28cdot 9+4 equiv 4mod 9} \u305d\u306e\u756a\u53f7\u3092\u9589\u3058\u307e\u3059 n = 9 {displaystyle n = 9} \u69cb\u6210\u3055\u308c\u3002 \u30d5\u30a7\u30eb\u30de\u30c3\u30c1\u30d7\u30e9\u30a4\u30e0\u30ca\u30c1\u30e5\u30e9\u30eb\u30c6\u30b9\u30c8\u306f\u6b21\u306e\u3088\u3046\u306b\u5b9f\u884c\u3055\u308c\u307e\u3059\uff1a \u3042\u306a\u305f\u304c\u5225\u308c\u306b\u5916\u56fd\u4eba\u3067\u306a\u3044\u5834\u5408\u3001\u7d50\u679c\u306f \u69cb\u6210 \u3002\u3055\u3082\u306a\u3044\u3068\uff1a \u3082\u3057\u3082 an\u22121\u2262 \u521d\u3081 \u306b\u5bfe\u3057\u3066 n {displaystyle a^{n-1} equiv1mod n} \u3001\u7d50\u679c\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059 \u69cb\u6210 \u3002 \u305d\u308c\u4ee5\u5916\u306e\u5834\u5408\u306f\u3001\u7d50\u679c\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059 \u58f0\u660e\u306f\u3042\u308a\u307e\u305b\u3093 \u30c6\u30b9\u30c8\u304c\u7570\u306a\u308b\u30d9\u30fc\u30b9\u3067\u6570\u56de\u7e70\u308a\u8fd4\u3055\u308c\u308b\u5834\u5408\u3001\u305d\u3046\u3067\u3059 \u58f0\u660e\u306f\u3042\u308a\u307e\u305b\u3093 \u89e3\u91c8\u53ef\u80fd\u3067\u3059 \u304a\u305d\u3089\u304f\u7d20\u6570 \u3002 \u305f\u3060\u3057\u3001\u81ea\u7136\u6570\u304c\u3042\u308a\u307e\u3059 n {displaystyle n} \u4e00\u6d41\u306e\u4eba\u7269\u3067\u306f\u306a\u304f\u3001\u975e\u5206\u5272\u30d9\u30fc\u30b9\u306e\u305f\u3081\u306b a {displaystyle a} \u305d\u308c\u3092\u9069\u7528\u3057\u307e\u3059 a n\u22121 –  \u521d\u3081 {displaystyle a^{n-1} -1} \u7d42\u3048\u305f n {displaystyle n} \u5206\u88c2\u53ef\u80fd\u3067\u3059\u3002\u305d\u306e\u3088\u3046\u306a\u6570\u5b57\u306f\u3001\u30d9\u30fc\u30b9\u306efermatsche pseudoprim\u756a\u53f7\u3068\u547c\u3070\u308c\u307e\u3059 a {displaystyle a} \u3002\u30ab\u30fc\u30de\u30a4\u30b1\u30eb\u306e\u6570\u306f\u3001\u7279\u306b\u9811\u56fa\u306a\u30d5\u30a1\u30fc\u30de\u30c3\u30c1\u30a7\u30fb\u30b7\u30e5\u30fc\u30c9\u30d7\u30ea\u30e0\u6570\u3067\u3059\u3002\u3053\u308c\u306f\u305d\u3046\u3067\u3059 a n\u22121 –  \u521d\u3081 {displaystyle a^{n-1} -1} \u305f\u3081\u306b \u306b \u306b n {displaystyle n} \u57fa\u5730\u3092\u901a\u308a\u629c\u3051\u307e\u3059 n {displaystyle n} \u5206\u88c2\u53ef\u80fd\u3002 \u30d9\u30fc\u30b9\u3067\u30d5\u30a7\u30e9\u30c4\u30b7\u30a7\u30f3\u30d7\u30e9\u30a4\u30e0\u30da\u30a4\u30c6\u30b9\u30c8\u3092\u4f7f\u7528\u3059\u308b\u5834\u5408 a = 2 {displaystyle a = 2} \u3001\u6570\u5b57\u304c\u7d20\u6570\u3067\u3042\u308b\u304b\u3069\u3046\u304b\u306f\u304b\u306a\u308a\u5b89\u5168\u306b\u6c7a\u5b9a\u3067\u304d\u307e\u3059\u3002\u6b21\u306e\u8868\u306f\u3001\u6570\u50243\u301c29\u306e\u8a08\u7b97\u306e\u7d50\u679c\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002 n{displaystyle n}3 4 5 6 7 8 9 \u5341 11 12\u756a\u76ee 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 2n\u22121modn{displaystyle 2^{n-1}{bmod {n}}}\u521d\u3081 0 \u521d\u3081 2 \u521d\u3081 0 4 2 \u521d\u3081 8 \u521d\u3081 2 4 0 \u521d\u3081 14 \u521d\u3081 8 4 2 \u521d\u3081 8 16 2 13 8 \u521d\u3081 \u3053\u306e\u30c6\u30fc\u30d6\u30eb\u306f\u6700\u65b0\u306e\u3082\u306e\u3067\u3059 n = 340 {displaystyle n = 340} \u7d99\u7d9a\u3055\u308c\u3001\u5e38\u306b\u5404\u30d7\u30e9\u30a4\u30e0\u756a\u53f7\u306e\u4e0b\u3067\u3001\u591a\u304f\u306e1\u3068\u591a\u6570\u306e\u7570\u306a\u308b\u6570\u304c\u7570\u306a\u308a\u307e\u3059\u3002 2 340 –  \u521d\u3081 {displaystyle 2^{340} -1} \u3001\u3057\u304b\u3057 341 = 11 de \u6700\u521d\u306b30 {displaystyle 341 = 11cdot 31} \u30d7\u30ea\u30e0\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002 \u305d\u308c\u307e\u3067 n = 2000 {displaystyle n = 2000} 303\u306e\u30d7\u30e9\u30a4\u30e0\u30ca\u30f3\u30d0\u30fc\u306f\u3042\u308a\u307e\u3059\u304c\u30012\u3064\u306eFermatsche Pseudoprim\u6570\u3001\u3064\u307e\u308a341\u3001561\u3001645\u30011105\u30011387\u30011729\u30011905\u306e\u307f\u304c\u3042\u308a\u307e\u3059\u304b\uff08\u7d50\u679c A001567 OEIS\u3067\uff09\u3002\u5225\u306e\u6839\u62e0\u3092\u9078\u629e\u3059\u308b\u3068\u3001\u540c\u69d8\u306e\u7d50\u679c\u304c\u5f97\u3089\u308c\u307e\u3059\u3002\u30dd\u30fc\u30eb\u30fb\u30a8\u30eb\u30c9\u30b9\u306b\u3088\u3063\u3066\u3001\u305d\u308c\u305e\u308c\u306e\u64ec\u4f3c\u30d7\u30e9\u30a4\u30e0\u6570\u304c\u30d7\u30e9\u30a4\u30e0\u30ca\u30f3\u30d0\u30fc\u3068\u6bd4\u8f03\u3057\u3066\u7121\u8996\u3067\u304d\u308b\u3053\u3068\u304c\u8a3c\u660e\u3055\u308c\u3066\u3044\u307e\u3059\uff08\u305d\u308c\u305e\u308c\u3054\u3068\u306b a {displaystyle a} Fermatsche Pseudoprim\u306e\u6570\u306e\u6570\u306f\u3088\u308a\u5c11\u306a\u3044\u3053\u3068\u304c\u9069\u7528\u3055\u308c\u307e\u3059 \u30d0\u30c4 {displaystyle x} \u3088\u308a\u5c0f\u3055\u3044\u7d20\u6570\u306e\u6570\u3067\u5272\u3063\u3066\u3044\u307e\u3059 \u30d0\u30c4 {displaystyle x} \u6210\u9577\u3059\u308b \u30d0\u30c4 {displaystyle x} \u30bc\u30ed\u306b\u5bfe\u3057\u3066\u53ce\u675f\u3057\u305f\uff09\u3002 \u30d9\u30fc\u30b92\u3092\u4f7f\u7528\u3059\u308b\u5834\u5408\u3001340\u756a\u307e\u3067\u6b63\u3057\u3044\u7d50\u679c\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3044\u304f\u3064\u304b\u306e\u30d9\u30fc\u30b9\uff082\u30013\u30015\u306a\u3069\uff09\u3067\u30c6\u30b9\u30c8\u3059\u308b\u3068\u3001\u5b89\u5168\u306a\u5236\u9650\u304c\u4e0a\u6607\u3057\u307e\u3059\u3002\u30d9\u30fc\u30b92\u30683\u306e\u30c6\u30b9\u30c8\u306f\u3001\u305f\u3068\u3048\u3070\u6700\u59271104\u307e\u3067\u6b63\u3057\u3044\u3067\u3059\u3002\u30d9\u30fc\u30b92\u30013\u30015\u3092\u4f7f\u7528\u3059\u308b\u3068\u3001\u5236\u9650\u306f1728\u306b\u5897\u52a0\u3057\u307e\u3059\u3002 \u5b9f\u969b\u306b\u306f\u3001\u4ed6\u306e\u4e3b\u8981\u306a\u652f\u6255\u3044\u304c\u671b\u307e\u3057\u3044\u3067\u3059\u3002 B. Miller-Selfridge-rabin\u30c6\u30b9\u30c8\u306f\u5f7c\u3089\u306e\u305f\u3081\u3067\u3059\u8907\u5408\u6570\u304c\u305d\u306e\u3088\u3046\u306b\u8a8d\u8b58\u3055\u308c\u3066\u3044\u306a\u3044\u5834\u5408\u3092\u9664\u5916\u3059\u308b\u53ef\u80fd\u6027\u304c\u9ad8\u304f\u306a\u308a\u307e\u3059\u3002 \u3057\u304b\u3057\u3001Fermatschen Prime Test\u306b\u306f\u3055\u3089\u306b\u958b\u767a\u304c\u3042\u308a\u307e\u3057\u305f\u30021983\u5e74\u304b\u3089\u3001\u6570\u5b66\u8005\u30ec\u30ca\u30fc\u30c9M. a dleman\u3001\u30ab\u30fc\u30eb p \u30aa\u30e2\u30e9\u30f3\u30b9\u3001\u30ed\u30d0\u30fc\u30c8 r \u3048\u3048\u3068\u3001H\u3002 c Ohen\u3068Hendrik W. l Ensstra Jr.\u5f7c\u3089\u306b\u3061\u306a\u3093\u3067\u540d\u4ed8\u3051\u3089\u308c\u307e\u3057\u305f APRCL\u30c6\u30b9\u30c8 \u524d\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\/19438#breadcrumbitem","name":"Fermatscher Prime FAG -Wikipedia"}}]}]