MathNet 2018-part-02 — 181 problems (EN–VI) Question 150

Let $p \geqslant 5$ be a prime number. Prove that there exists an integer $n$ such that for every $x \in \{n-1, n, n+1\}$, $p^{2} \nmid x^{p-1}-1$ and $p \nmid x$.