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Italian Mathematical Olympiad

Number theory Difficulty 5.0 AIME, harder Prove it Italy

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

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.