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 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.

Read more about Carmichael's Totient Function Conjecture: Examples, Lower Bounds, Other Results

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