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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Mirimanoff's congruence ： ウィキペディア英語版 Mirimanoff's congruence In number theory, a branch of mathematics, a Mirimanoff's congruence is one of a collection of expressions in modular arithmetic which, if they hold, entail the truth of Fermat's Last Theorem. Since the theorem has now been proven, these are now of mainly historical significance, though the Mirimanoff polynomials are interesting in their own right. The theorem is due to Dmitry Mirimanoff. ==Definition== The ''n''th Mirimanoff polynomial for the prime ''p'' is :$\backslash phi\_n(t)\; =\; 1^t\; +\; 2^t^2\; +\; ...\; +\; (p-1)^\; t^.$ In terms of these polynomials, if ''t'' is one of the six values where ''X''''p''+''Y''''p''+''Z''''p''=0 is a solution to Fermat's Last Theorem, then * φ''p''-1(''t'') ≡ 0 (mod ''p'') * φ''p''-2(''t'')φ2(''t'') ≡ 0 (mod ''p'') * φ''p''-3(''t'')φ3(''t'') ≡ 0 (mod ''p'') :... * φ(''p''+1)/2(''t'')φ(''p''-1)/2(''t'') ≡ 0 (mod ''p'') 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Mirimanoff's congruence」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.