RO-NMO 2003 Problem 81

Let $m,n$ be positive integers. Prove that the number $5^n+5^m$ can be represented as sum of two perfect squares if and only if $n-m$ is even.

Vasile Zidaru

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.