Maths Olympiad Prep

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Number theory Difficulty 5.0 AIME, harder Prove it Italy

Given a prime number pp, determine all ordered pairs of natural numbers (m,n)(m, n) satisfying the equation:
1m+1n=1p \frac{1}{m} + \frac{1}{n} = \frac{1}{p}

Solution

SOLUTION

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Source: MathNet, licensed CC-BY-4.0. Statement translated into English from it; metadata (topic, difficulty) added by this project.