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Any subset ''R'' of the integers is called a reduced residue system modulo ''n'' if #gcd(''r'', ''n'') = 1 for each ''r'' contained in ''R''; #''R'' contains φ(''n'') elements; #no two elements of ''R'' are congruent modulo ''n''. Here denotes Euler's totient function. A reduced residue system modulo ''n'' can be formed from a complete residue system modulo ''n'' by removing all integers not relatively prime to ''n''. For example, a complete residue system modulo 12 is . 1, 5, 7 and 11 are the only integers in this set which are relatively prime to 12, and so the corresponding reduced residue system modulo 12 is . The cardinality of this set can be calculated with the totient function: . Some other reduced residue systems modulo 12 are: * * * * ==Facts== *If is a reduced residue system with ''n'' > 2, then . *Every number in a reduced residue system mod ''n'' is a generator for the additive group of integers modulo n. 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「reduced residue system」の詳細全文を読む スポンサード リンク
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