MathNet 2007-part-02 — 187 problems (EN–VI) Question 94

Let $n \gt 1$ be a positive integer and $p$ a prime number such that $n \mid (p-1)$ and $p \mid \left(n^{6}-1\right)$. Prove that at least one of the numbers $p-n$ and $p+n$ is a perfect square.