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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 Legendre's formula ： ウィキペディア英語版 Legendre's formula In mathematics, Legendre's formula gives an expression for the exponent of the largest power of a prime ''p'' that divides the factorial $n!$. It is named for Adrien-Marie Legendre. == Statement == Let ''p'' be a prime and ''n'' be a positive integer. Let $\backslash nu\_p(n)$ denote the ''p''-adic valuation of ''n''. Then :$\backslash nu\_p(n!)\; =\; \backslash sum\_^\; \backslash left\backslash lfloor\; \backslash frac\; \backslash right\backslash rfloor,$ where $\backslash lfloor\; x\; \backslash rfloor$ is the floor function. Equivalently, if $s\_p(n)$ denotes the sum of the standard base-''p'' digits of ''n'', then :$\backslash nu\_p(n!)\; =\; \backslash frac.$ 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「Legendre's formula」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.