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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 Agoh–Giuga conjecture ： ウィキペディア英語版 Agoh–Giuga conjecture In number theory the Agoh–Giuga conjecture on the Bernoulli numbers ''B''''k'' postulates that ''p'' is a prime number if and only if :$pB\_\; \backslash equiv\; -1\; \backslash pmod\; p.$ It is named after Takashi Agoh and Giuseppe Giuga. ==Equivalent formulation== The conjecture as stated above is due to Takashi Agoh (1990); an equivalent formulation is due to Giuseppe Giuga, from 1950, to the effect that ''p'' is prime if :$1^+2^+\; \backslash cdots\; +(p-1)^\; \backslash equiv\; -1\; \backslash pmod\; p$ which may also be written as :$\backslash sum\_^\; i^\; \backslash equiv\; -1\; \backslash pmod\; p.$ It is trivial to show that ''p'' being prime is sufficient for the second equivalence to hold, since if ''p'' is prime, Fermat's little theorem states that :$a^\; \backslash equiv\; 1\; \backslash pmod\; p$ for $a\; =\; 1,2,\backslash dots,p-1$, and the equivalence follows, since $p-1\; \backslash equiv\; -1\; \backslash pmod\; p.$ 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「Agoh–Giuga conjecture」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.