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

Huan Xiao

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

Number Theory 2019-07-02 v2

Authors: Huan Xiao

Abstract

The Euler's totient function $\varphi(n)$ 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 $\varphi(n)\mid n-1$ . We also note that there are infinitely many primes that are not Sophie Germain primes.

Keywords

prime numbers prime number theory multiplicative functions

Cite

@article{arxiv.1711.08313,
  title  = {On the Lehmer's problem involving Euler's totient function},
  author = {Huan Xiao},
  journal= {arXiv preprint arXiv:1711.08313},
  year   = {2019}
}

Comments

There is an error in the proof of Theorem 2.3

Related papers

View all related →