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In mathematics, '''Carmichael's totient function conjecture''' concerns the [[Multiplicity (mathematics)|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 Daniel Carmichael|Robert Carmichael]] first stated this conjecture 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==
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