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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 Multiplicative order ： ウィキペディア英語版 Multiplicative order In number theory, given an integer ''a'' and a positive integer ''n'' with gcd(''a'',''n'') = 1, the multiplicative order of ''a'' modulo ''n'' is the smallest positive integer ''k'' with : ''a''''k'' ≡ 1 (mod ''n''). In other words, the multiplicative order of ''a'' modulo ''n'' is the order of ''a'' in the multiplicative group of the units in the ring of the integers modulo ''n''. The order of ''a'' modulo ''n'' is usually written ord''n''(''a''), or O''n''(''a''). == Example == The powers of 4 modulo 7 are as follows: : $\backslash begin$ 4^0 &= 1 &=0 \times 7 + 1 &\equiv 1\pmod7 \\ 4^1 &= 4 &=0 \times 7 + 4 &\equiv 4\pmod7 \\ 4^2 &= 16 &=2 \times 7 + 2 &\equiv 2\pmod7 \\ 4^3 &= 64 &=9 \times 7 + 1 &\equiv 1\pmod7 \\ 4^4 &= 256 &=36 \times 7 + 4 &\equiv 4\pmod7 \\ 4^5 &= 1024 &=146 \times 7 + 2 &\equiv 2\pmod7 \\ \end : $\backslash text$ The smallest positive integer ''k'' such that 4''k'' = 1 (mod 7) is 3, so O7(4) = 3. 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「Multiplicative order」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.