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(p+m)/(p+n)= m/n + 1/p^2

Source: 2017 Swedish Mathematical Competition p2

May 1, 2021
number theoryDiophantine equationdiophantine

Problem Statement

Let pp be a prime number. Find all pairs of coprime positive integers (m,n)(m,n) such that p+mp+n=mn+1p2. \frac{p+m}{p+n}=\frac{m}{n}+\frac{1}{p^2}.
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