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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 Gauss's lemma (number theory) ： ウィキペディア英語版 Gauss's lemma (number theory) Gauss's lemma in number theory gives a condition for an integer to be a quadratic residue. Although it is not useful computationally, it has theoretical significance, being involved in some proofs of quadratic reciprocity. It made its first appearance in Carl Friedrich Gauss's third proof (1808) of quadratic reciprocity and he proved it again in his fifth proof (1818).〔 == Statement of the lemma == For any odd prime let be an integer that is coprime to . Consider the integers :$a,\; 2a,\; 3a,\; \backslash dots,\; \backslash fraca$ and their least positive residues modulo . (These residues are all distinct, so there are ( of them.) Let be the number of these residues that are greater than . Then :$\backslash left(\backslash frac\backslash right)\; =\; (-1)^n,$ where $\backslash left(\backslash frac\backslash right)$ is the Legendre symbol. 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「Gauss's lemma (number theory)」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.