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

Huan Xiao

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arXiv · 1711.08313

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

Huan Xiao

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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.

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Huan Xiao. 2017-11-16. On the Lehmer's problem involving Euler's totient function. https://arxiv.org/abs/1711.08313

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