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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 Root of unity modulo n ： ウィキペディア英語版 Root of unity modulo n In mathematics, namely ring theory, a ''k''-th root of unity modulo ''n'' for positive integers ''k'', ''n'' ≥ 2, is a solution ''x'' to the equation (or ''congruence'') $x^k\; \backslash equiv\; 1\; \backslash pmod$. If ''k'' is the smallest such exponent for ''x'', then ''x'' is called a primitive ''k''-th root of unity modulo ''n''.〔 〕 See modular arithmetic for notation and terminology. Do not confuse this with a primitive element modulo ''n'', where the primitive element must generate all units of the residue class ring $\backslash mathbb/n\backslash mathbb$ by exponentiation. That is, there are always roots and primitive roots of unity modulo ''n'' for ''n'' ≥ 2, but for some ''n'' there is no primitive element modulo ''n''. Being a root or a primitive root modulo ''n'' always depends on the exponent ''k'' and the modulus ''n'', whereas being a primitive element modulo ''n'' only depends on the modulus ''n'' — the exponent is automatically $\backslash varphi(n)$. == Roots of unity == 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「Root of unity modulo n」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.