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Infinitely many pairs satisfy divisibility relation

Source: Germany 2003- Problem 6

December 11, 2022
number theorycoprimeDivisibilitypairsinfinitely many solutions

Problem Statement

Prove that there are infinitely many coprime, positive integers a,ba,b such that aa divides b2−5b^2 -5 and bb divides a2−5.a^2 -5.
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