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NT about non-squarefree integers

Source: ARO 2021 10.7/9.7

April 20, 2021
number theoryRussiaAll Russian Olympiad

Problem Statement

Given are positive integers n>20n>20 and k>1k>1, such that k2k^2 divides nn. Prove that there exist positive integers a,b,ca, b, c, such that n=ab+bc+can=ab+bc+ca.
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