MathNet 2015-part-05 — 191 problems (EN–VI) Question 100

Let $p$, $q$ be two different odd prime numbers and $n$ an integer such that $p q$ divides $n^{p q} + 1$. Prove that if $p^{3} q^{3}$ divides $n^{p q} + 1$ then either $p^{2}$ divides $n + 1$ or $q^{2}$ divides $n + 1$.