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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 Lucas's theorem ： ウィキペディア英語版 Lucas' theorem In number theory, Lucas's theorem expresses the remainder of division of the binomial coefficient $\backslash tbinom$ by a prime number ''p'' in terms of the base ''p'' expansions of the integers ''m'' and ''n''. Lucas's theorem first appeared in 1878 in papers by Édouard Lucas.〔 * (part 1); * (part 2); * (part 3)〕 == Formulation == For non-negative integers ''m'' and ''n'' and a prime ''p'', the following congruence relation holds: :$\backslash binom\backslash equiv\backslash prod\_^k\backslash binom\backslash pmod\; p,$ where :$m=m\_kp^k+m\_p^+\backslash cdots\; +m\_1p+m\_0,$ and :$n=n\_kp^k+n\_p^+\backslash cdots\; +n\_1p+n\_0$ are the base ''p'' expansions of ''m'' and ''n'' respectively. This uses the convention that $\backslash tbinom$ = 0 if ''m'' < ''n''. 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「Lucas' theorem」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.