On the Lehmer's problem involving Euler's totient function

Abstract

The Euler's totient function $\phi (n)$ counts the positive integers up to a given integer $n$ that are relatively prime to $n$. We solve a problem due to Lehmer that there is no composite number $n$ such that $\phi (n)\mid n-1$. We also note that there are infinitely many primes that are not Sophie Germain primes.

arXiv commentThere is an error in the proof of Theorem 2.3