MathNet 2015-part-05 — 191 problems (EN–VI) Question 103

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.