MathDB

1

Part of 2012 Kyrgyzstan National Olympiad

Problems(1)

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

Source: Kyrgyzstan 2012, Problem 1

5/2/2013
Prove that n n must be prime in order to have only one solution to the equation 1x−1y=1n\frac{1}{x}-\frac{1}{y}=\frac{1}{n}, x,y∈Nx,y\in\mathbb{N}.
number theory unsolvednumber theory