MathNet 2018-part-04 — 181 problems (EN–VI) Question 71

Let $p$ be a prime number greater than $5$ and $S=\{p-n^{2} \mid n \in \mathbb{N}, n^{2}\lt p\}$. Prove that $S$ contains two elements $a$ and $b$ such that $1\lt a\lt b$ and $a$ divides $b$.