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A little play with divisors

Source: European Mathematical Cup 2022, Junior Division, Problem 1

December 19, 2022
number theorymodular arithmeticDivisibilityDivisors

Problem Statement

Determine all positive integers nn for which there exist positive divisors aa, bb, cc of nn such that a>b>ca>b>c and a2−b2a^2 - b^2, b2−c2b^2 - c^2, a2−c2a^2 - c^2 are also divisors of nn.
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