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.