The positive $n > 3$ called ‘nice’ if and only if $n +1$ and $8n + 1$ are both perfect squares. How many positive integers $k \le 15$ such that $4n + k$ are composites for all nice numbers $n$?
Source: 2022 Saudi Arabia JBMO TST 1.1
Tags: number theory, Perfect Squares
The positive $n > 3$ called ‘nice’ if and only if $n +1$ and $8n + 1$ are both perfect squares. How many positive integers $k \le 15$ such that $4n + k$ are composites for all nice numbers $n$?