Carmichael's totient function conjecture: Difference between revisions

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{{short description|mathematics concept}}

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 (mathematics)|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]].