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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: : : 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
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