SE-SKOLORNAS 1973 Problem 4

$p$ is a prime. Find all relatively prime positive integers $m$ , $n$ such that $\frac{m}{n}+\frac{1}{p^2}=\frac{m+p}{n+p}$

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.