[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/10531#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/10531","headline":"Kubikzahl-\u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2","name":"Kubikzahl-\u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2","description":"n\u00b3=n\u22c5n\u22c5n \u4e00 \u7acb\u65b9\u4f53\u756a\u53f7 \uff08\u304b\u3089 \u30e9\u30c6\u30f3 \u30ad\u30e5\u30fc\u30d0\u30b9 \u3001\u300cCube\u300d\uff09\u306f\u3001\u81ea\u7136\u6570\u306b2\u56de\u81ea\u5206\u306b\u4e57\u7b97\u3059\u308b\u3068\u767a\u751f\u3059\u308b\u6570\u5b57\u3067\u3059\u3002\u305f\u3068\u3048\u3070\u3001\u3067\u3059 27 = 3 de 3 de 3 {displaystyle 27 = 3cdot 3cdot 3}","datePublished":"2021-05-28","dateModified":"2021-05-28","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/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\/16ee64dd3c392173381add1fffcbd31712164fd2","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/16ee64dd3c392173381add1fffcbd31712164fd2","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/10531","wordCount":6984,"articleBody":"n\u00b3=n\u22c5n\u22c5n \u4e00 \u7acb\u65b9\u4f53\u756a\u53f7 \uff08\u304b\u3089 \u30e9\u30c6\u30f3  \u30ad\u30e5\u30fc\u30d0\u30b9 \u3001\u300cCube\u300d\uff09\u306f\u3001\u81ea\u7136\u6570\u306b2\u56de\u81ea\u5206\u306b\u4e57\u7b97\u3059\u308b\u3068\u767a\u751f\u3059\u308b\u6570\u5b57\u3067\u3059\u3002\u305f\u3068\u3048\u3070\u3001\u3067\u3059 27 = 3 de 3 de 3 {displaystyle 27 = 3cdot 3cdot 3} \u591a\u304f\u306e\u7acb\u65b9\u4f53\u3002\u6700\u521d\u306e\u7acb\u65b9\u4f53\u6570\u306f\u3067\u3059 0\u30011\u30018\u300127\u300164\u3001125\u3001216\u3001343\u3001512\u3001729\u30011000\u3001…\uff08\u7d50\u679c A000578 OEIS\u3067\uff09 \u4e00\u90e8\u306e\u8457\u8005\u306e\u5834\u5408\u3001\u30bc\u30ed\u306f\u591a\u304f\u306e\u7acb\u65b9\u4f53\u3067\u306f\u306a\u3044\u305f\u3081\u3001\u6570\u5024\u306e\u6570\u306f1\u3064\u3060\u3051\u3067\u59cb\u307e\u308a\u307e\u3059\u3002 \u7acb\u65b9\u4f53\u6570\u3068\u3044\u3046\u7528\u8a9e\u306f\u3001\u30ad\u30e5\u30fc\u30d6\u306e\u5e7e\u4f55\u5b66\u7684\u56f3\u304b\u3089\u6d3e\u751f\u3057\u3066\u3044\u307e\u3059\u3002\u30ad\u30e5\u30fc\u30d6\u3092\u69cb\u7bc9\u3059\u308b\u305f\u3081\u306b\u5fc5\u8981\u306a\u77f3\u306e\u6570\u306f\u3001\u5e38\u306b\u591a\u304f\u306e\u7acb\u65b9\u4f53\u306b\u5bfe\u5fdc\u3057\u3066\u3044\u307e\u3059\u3002\u305f\u3068\u3048\u3070\u3001\u30b5\u30a4\u30c9\u95773\u306e\u30ad\u30e5\u30fc\u30d6\u306f27\u306e\u77f3\u3092\u4f7f\u7528\u3057\u3066\u914d\u7f6e\u3067\u304d\u307e\u3059\u3002 \u5e7e\u4f55\u5b66\u7684\u306a\u4eba\u7269\u3068\u306e\u3053\u306e\u95a2\u4fc2\u306b\u3088\u308a\u3001\u7acb\u65b9\u4f53\u6570\u306f\u6570\u5b57\u306e1\u3064\u3067\u3042\u308a\u3001\u6b63\u65b9\u5f62\u306e\u6570\u5b57\u3068\u56db\u9762\u4f53\u306e\u6570\u3082\u542b\u307e\u308c\u307e\u3059\u3002 1\u30012\u30013\u30014\u30015\u304b\u3089\u306e\u9023\u7d9a\u3057\u305f\u30d6\u30ed\u30c3\u30af\u304b\u3089\u2026\u4e0a\u6607\u3059\u308b\u9806\u5e8f\u3067\u5947\u5999\u306a\u81ea\u7136\u6570\u30011\u7acb\u65b9\u6570\u306f\u5408\u8a08\u306b\u3088\u3063\u3066\u751f\u6210\u3067\u304d\u307e\u3059\u30021\u23df1\u00a03\u00a05\u23df8\u00a07\u00a09\u00a011\u23df27\u00a013\u00a015\u00a017\u00a019\u23df64\u00a021\u00a023\u00a025\u00a027\u00a029\u23df125\u00a0\u2026{displaystyle underbrace {1} _ {1}\u30a2\u30f3\u30c0\u30fc\u30d6\u30ec\u30fc\u30b9{3 5} _ {8} underbrace {7 9 11} _ {27}\u30a2\u30f3\u30c0\u30fc\u30d6\u30ec\u30fc\u30b9{13 15 17 19} _ {64}\u30a2\u30f3\u30c0\u30fc\u30d6\u30ec\u30fc\u30b9{21 \u4e2d\u592e\u306b\u3042\u308b6\u3064\u306e6 -6\u306e\u756a\u53f71\u30017\u300119\u300137\u300161\u300191\u3001127\u3001169\u3001217\u3001271\u3001…\u306e\u7d50\u679c\u306b\u57fa\u3065\u3044\u3066… n {displaystyle n} -e\u6700\u521d\u306e\u3082\u306e\u306e\u5408\u8a08\u3068\u3057\u3066\u306ee\u7acb\u65b9\u6570 n {displaystyle n} \u6b21\u306e\u30e1\u30f3\u30d0\u30fc\uff1a 1=18=1+727=1+7+1964=1+7+19+37125=1+7+19+37+61\u2026=\u2026{displaystyle {begin {aligned} 1\uff06= 1 \\ 8\uff06= 1+7 \\ 27\uff06= 1+7+19 \\ 64\uff06= 1+7+19+37 \\ 125\uff06= 1+7+19+37+61 \\ ldots\uff06= ldots end {aligned}}}}}}}} \u6700\u521d\u306e\u5408\u8a08 n {displaystyle n} \u7acb\u65b9\u4f53\u6570\u306f\u3001\u306e\u6b63\u65b9\u5f62\u306b\u7b49\u3057\u304f\u306a\u308a\u307e\u3059 n {displaystyle n}  – \u30c6\u30f3\u30c8\u30e9\u30a4\u30a2\u30f3\u30b0\u30eb\u756a\u53f7\uff1a \u2211i=1ni3=13+23+\u2026+n3=(n(n+1)2)2{displaystyle sum _ {i = 1}^{n} i^{3} = 1^{3}+2^{3}+ldots+n^{3} = left\uff08{frac {n+1\uff09} {2}}\u53f3\uff09^{2}}}} \u5404\u81ea\u7136\u6570\u306f\u3001\u6700\u59279\u7acb\u65b9\u6570\u5024\u306e\u5408\u8a08\u3068\u3057\u3066\u63d0\u793a\u3067\u304d\u307e\u3059\uff08\u6307\u65703\u306e\u8b66\u6212\u554f\u984c\u306e\u89e3\u6c7a\u7b56\uff09\u3002 23\u756a\u306f\u30019\u3064\u306e\u590f\u304c\u5fc5\u8981\u306b\u306a\u308b\u53ef\u80fd\u6027\u304c\u3042\u308b\u3053\u3068\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u306b\u306f\u30d7\u30ec\u30bc\u30f3\u30c6\u30fc\u30b7\u30e7\u30f3\u304c\u3042\u308a\u307e\u3059  23 = 8 + 8 + \u521d\u3081 + \u521d\u3081 + \u521d\u3081 + \u521d\u3081 + \u521d\u3081 + \u521d\u3081 + \u521d\u3081 {displaystyle 23 = 8+8+1+1+1+1+1+1+1\u3001} \u3001 \u3057\u304b\u3057\u3001\u660e\u3089\u304b\u306b\u3001\u305d\u308c\u4ee5\u4e0b\u306e\u7acb\u65b9\u4f53\u306e\u30b5\u30de\u30f3\u30c9\u3092\u6301\u3064\u3082\u306e\u306f\u3042\u308a\u307e\u305b\u3093\u3002 \u5404\u7acb\u65b9\u4f53\u6570\u306f\u30012\u3064\u306e\u9023\u7d9a\u3057\u305f\u4e8c\u91cd\u4e09\u89d2\u5f62\u306e\u6570\u306e\u9593\u306e\u5947\u6570\u6570\u306e\u5408\u8a08\u3068\u30012\u3064\u306e\u4e09\u89d2\u5f62\u6570\u306e\u6b63\u65b9\u5f62\u306e\u5dee\u3068\u3057\u3066\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002n3=\u2211i=1n(n\u22121)n+2i\u22121=\u0394n2\u2212\u0394n\u221212{displaystyle n^{3} = sum _ {i = 1}^{n}\uff08n-1\uff09n+2i-1 = {delta _ {n}}^{2}  –  {delta _ {n-1}}^}^}}}}}}}}}} 2\u3064\u306e\u7acb\u65b9\u4f53\u6570\u306e\u5408\u8a08\u306f\u3001\u7acb\u65b9\u4f53\u306e\u6570\u5b57\u3067\u3055\u3048\u3042\u308a\u307e\u305b\u3093\u3002\u8a00\u3044\u63db\u3048\u308c\u3070\u3001\u3053\u308c\u306f\u65b9\u7a0b\u5f0f\u3092\u610f\u5473\u3057\u307e\u3059  a3+ b3= c3{displaystyle a^{3}+b^{3} = c^{3}\u3001} \u81ea\u7136\u6570\u306e\u89e3\u6c7a\u7b56\u306f\u3042\u308a\u307e\u305b\u3093 a \u3001 b \u3001 c {displaystyle a\u3001b\u3001c} \u6240\u6709\u3002 Fermatschen Guess\u306e\u3053\u306e\u7279\u5225\u306a\u30b1\u30fc\u30b9\u306f\u30011753\u5e74\u306bLeonhard Euler\u306b\u3088\u3063\u3066\u8a3c\u660e\u3055\u308c\u307e\u3057\u305f\u3002\u6b21\u306e\u4f8b\u304c\u793a\u3059\u3088\u3046\u306b\u30012\u3064\u4ee5\u4e0a\u306e\u590f\u3092\u8a31\u53ef\u3059\u308b\u5834\u5408\u3001\u30ad\u30e5\u30fc\u30d6\u306e\u5408\u8a08\u3068\u3057\u3066\u591a\u304f\u306e\u30ad\u30e5\u30fc\u30d6\u3092\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059\uff08\u76f4\u63a5\u9023\u7d9a\u3057\u305f3\u3064\u306e\u7acb\u65b9\u4f53\u6570\u304c3\u3064\u3042\u308a\u307e\u3059\uff09\uff1a  33+ 43+ 53= 63{displaystyle 3^{3}+4^{3}+5^{3} = 6^{3}\u3001} \u3002 \u7acb\u65b9\u4f53\u6570\u306e\u7d50\u679c\u304b\u3089\u30e2\u30b8\u30e5\u30fc\u30eb9\u3092\u53d6\u5f97\u3059\u308b\u3068\u3001\u5b9a\u671f\u7684\u306a\u30b7\u30fc\u30b1\u30f3\u30b9\u304c\u53d6\u5f97\u3055\u308c\u307e\u3059 0 \u3001 \u521d\u3081 \u3001 8 \u3001 … {displaystyle 0,1,8\u3001ldots} \uff08\u7d50\u679c A167176 OEIS\u3067\uff09\u3002\u3053\u308c\u306f\u304b\u3089\u3067\u3059 x3mod9= \uff08 \u30d0\u30c4 mod3)3\u3001 d = { \u30d0\u30c4 \u2208 Z} {displaystyle x^{3} {b in a a a a a a a a a a a a a a a a a a \u3002\u3053\u308c\u306f\u307e\u305f\u30013\u3064\u306e\u7acb\u65b9\u4f53\u6570\u306e\u5408\u8a08\u3068\u3057\u3066\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u6570\u5024\u306f\u30014\u307e\u305f\u306f5 mod 9\u3068\u4e00\u81f4\u3059\u308b\u3053\u3068\u306f\u6c7a\u3057\u3066\u306a\u3044\u3068\u7d50\u8ad6\u4ed8\u3051\u3066\u3044\u307e\u3059\u3002 \u3059\u3079\u3066\u306e\u7acb\u65b9\u4f53\u6570\u306e\u76f8\u4e92\u5024\u306e\u5408\u8a08\u306f\u3001Aperitif\u3068\u547c\u3070\u308c\u307e\u3059\u3002 Riemannschen\u306e\u4fa1\u5024\u306b\u5bfe\u5fdc\u3057\u307e\u3059 z {displaystyle zeta}  – \u6a5f\u80fd3\u3002 \u2211n=1\u221e1n3= z (3)= 1.202 0569 … {displaystyle sum _ {n = 1}^{infty} {frac {1} {n^{3}}} = zeta {\uff083\uff09} = 1 {\u3001} 2020569ldots} \u5168\u4f53\uff08\u307e\u305f\u306f\u5b9f\u969b\u306e\uff09\u6570\u306e\u5404\u30a8\u30d4\u30bd\u30fc\u30c9 \uff08 a i\uff09\uff09 i\u22650{displaystyle\uff08a_ {i}\uff09_ {igeq 0}} \u6b63\u5f0f\u306a\u4e00\u9023\u306e\u5897\u5f37\u3092\u5272\u308a\u5f53\u3066\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 \u2211i\u22650aixi{displaystyle textStyle sum _ {igeq 0} a_ {i} x^{i}} \u3002\u305f\u3060\u3057\u3001\u3053\u306e\u30b3\u30f3\u30c6\u30ad\u30b9\u30c8\u3067\u306f\u30010\u3067\u7acb\u65b9\u4f53\u6570\u306e\u7d50\u679c\u3001\u3064\u307e\u308a\u7d50\u679c\u3092\u958b\u59cb\u3059\u308b\u3053\u3068\u304c\u4e00\u822c\u7684\u3067\u3059\u3002 0 \u3001 \u521d\u3081 \u3001 8 \u3001 27 \u3001 \u516d\u5341\u56db \u3001 … {displaystyle 0,1,8,27,64\u3001ldots} \u691c\u8a0e\u3002\u305d\u306e\u5834\u5408\u3001\u7acb\u65b9\u4f53\u6570\u306e\u751f\u6210\u95a2\u6570\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059 \u2211i\u22650i3xi= \u30d0\u30c4 + 8 x2+ 27 x3+ \u516d\u5341\u56db x4+ … = x(x2+4x+1)(x\u22121)4{displaystyle sum _ {igeq 0} i^{3} x^{i} = x+8x^{2}+27x^{3}+64x^{4}+ldots = {frac {x\uff08x^{2}+4x+1\uff09}} {\uff08x-1\uff09^{4}}}} \u7acb\u65b9\u4f53\u756a\u53f7 a 3{displaystyle a^{3}} \u30d9\u30fc\u30b9\u3067\u3059 a {displaystyle a} \u5b9f\u6570\u3068\u6307\u6570 3 {displaystyle 3} \u6b63\u306e\u6570\u3002\u3053\u306e\u305f\u3081\u3001\u306e\u52b9\u529b\u5024 a 3{displaystyle a^{3}} \u30b5\u30fc\u30af\u30eb\u3068\u30eb\u30fc\u30e9\u30fc\u3092\u5099\u3048\u305f\u69cb\u9020\u3068\u3057\u3066\u306e\u591a\u304f\u306e\u6570\u5b57\u306b\u3064\u3044\u3066\u3002 \u57fa\u790e\u3067\u3042\u308c\u3001\u533a\u5225\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059 a {displaystyle a} \u6570\u3088\u308a\u5927\u304d\u3044\u307e\u305f\u306f\u5c0f\u3055\u3044 \u521d\u3081 {displaystyle1} \u306f\u3002\u4e21\u65b9\u306e\u30aa\u30d7\u30b7\u30e7\u30f3\u3092\u4ee5\u4e0b\u306b\u8aac\u660e\u3057\u307e\u3059\u3002 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