MathNet 2018-part-04 — 181 problems (EN–VI) Question 101

Let $p \gt 5$ be a prime number 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 $b$.

BMO, 1996