MathNet 2023-part-04 — 191 problems (EN–VI) Question 4

Let $n$, $m$, $k$ be integers such that $\frac{mk+n}{n^2+1}$ and $\frac{nk+m}{m^2+1}$ are integers. Show that $k^2 - 1$ is divisible by the greatest common divisor of $n^2+1$ and $m^2+1$.