# Thread: phi(n) divides n-1 implies n is prime

1. ## phi(n) divides n-1 implies n is prime

Prove that if $\phi(n)|(n-1)$ then $n$ is prime, where $\phi(n)$. is the Euler's totient function.

I am able to show that $n$ is square-free under the above condition.

2. ## Re: phi(n) divides n-1 implies n is prime

Originally Posted by abhishekkgp
Prove that if $\phi(n)|(n-1)$ then $n$ is prime, where $\phi(n)$. is the Euler's totient function.

I am able to show that $n$ is square-free under the above condition.
Lehmer's conjecture

3. ## Re: phi(n) divides n-1 implies n is prime

Originally Posted by princeps
Thank You. I did not know its an unsolved problem or I would not post it.

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### n is prime iff phi of n is n-1

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