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In mathematics, Carmichael's totient function conjecture concerns the multiplicity of values of Euler's totient function φ(''n''), which counts the number of integers less than and coprime to ''n''. It states that, for every ''n'' there is at least one other integer ''m'' ≠ ''n'' such that φ(''m'') = φ(''n''). Robert Carmichael first stated this conjecture in 1907, but as a theorem rather than as a conjecture. However, his proof was faulty and in 1922 he retracted his claim and stated the conjecture as an open problem. ==Examples== The totient function φ(''n'') is equal to 2 when ''n'' is one of the three values 3, 4, and 6. Thus, if we take any one of these three values as ''n'', then either of the other two values can be used as the ''m'' for which φ(''m'') = φ(''n''). Similarly, the totient is equal to 4 when ''n'' is one of the four values 5, 8, 10, and 12, and it is equal to 6 when ''n'' is one of the four values 7, 9, 14, and 18. In each case, there is more than one value of ''n'' having the same value of φ(''n''). The conjecture states that this phenomenon of repeated values holds for every ''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「Carmichael's totient function conjecture」の詳細全文を読む スポンサード リンク
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