NL-NWO 1996 Problem 2

Investigate whether for two positive integers $m$ and $n$ the numbers $m^2 + n$ and $n^2 + m$ can be both squares of integers.

Dataset text AI-MO AoPS. 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.