Lehmer's totient problem asks whether there is any composite number $n$ such that Euler's totient function $φ(n)$ divides $n − 1$. which it is unsolved problem or we may reformulate that question as : if $φ(n)$ divides $n − 1$ then $n$ must be a prime , Now my question here is : Assume a such counter example of that problem exists could we have more counter examples for it ?
if such counter example to Lehmer's totient problem exists then could we have more counter examples?
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2It is known that a solution must be a Carmichael number with at least $14$ prime factors. So, if we find a solution, we cannot immediately construct another. I think, several counterexamples could exist, perhaps even infinite many. I am not aware of an argument ruling that out. – Peter Jun 04 '20 at 06:57