Let $n$ and $k$ be two positive integers. Prove that if $n$ is relatively prime with $30$, then there exist two integers $a$ and $b$, each relatively prime with $n$, such that $\frac{a^2 - b^2 + k}{n}$ is an integer. Malik Talbi
Source: 2015 Saudi Arabia IMO TST I p3
Tags: number theory, Integer
Let $n$ and $k$ be two positive integers. Prove that if $n$ is relatively prime with $30$, then there exist two integers $a$ and $b$, each relatively prime with $n$, such that $\frac{a^2 - b^2 + k}{n}$ is an integer. Malik Talbi