HMMT 2020 T9

Let $p>5$ be a prime number. Show that there exists a prime number $q<p$ and a positive integer $n$ such that $p$ divides $n^{2}-q$ .

Dataset text NuminaMath olympiads. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.