BG-MO 2013 Problem 1

Find all prime numbers $p,q$ , for which $p^{q+1}+q^{p+1}$ is a perfect square.

Proposed by P. Boyvalenkov

Dataset text AoPS wiki problems. 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.