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Only one solution to 1/x - 1/y = 1/n

Source: Kyrgyzstan 2012, Problem 1

May 2, 2013

number theory unsolvednumber theory

Problem Statement

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}