OSN 2019 Problem 7

Determine all solutions of $x + y^2 = p^m$ $x^2 + y = p^n$ For $x,y,m,n$ positive integers and $p$ being a prime.

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.