Fall 2016, problem 25
Let $n,p$ be integers such that $n>1$ and $p$ is a prime. If $n\mid p-1$ and $p\mid n^3-1$, show that $4p-3$ is a perfect square.
Let $n,p$ be integers such that $n>1$ and $p$ is a prime. If $n\mid p-1$ and $p\mid n^3-1$, show that $4p-3$ is a perfect square.