KG-MO 2012 Problem 1

Prove that $n$ must be prime in order to have only one solution to the equation $\frac{1}{x}-\frac{1}{y}=\frac{1}{n}$ , $x,y\in\mathbb{N}$ .

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.