Problem

Source: Indian Postal Coaching 2008 set 4 p2

Tags: number theory, primes, prime, prime numbers, divides



Prove that an integer $n \ge 2$ is a prime if and only if $\phi (n)$ divides $(n - 1)$ and $(n + 1)$ divides $\sigma (n)$. [Here $\phi$ is the Totient function and $\sigma $ is the divisor - sum function.]

HIDE: Hint $n$ is squarefree