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nice diophantine with existence

Source: IMOC 2020 N2

August 13, 2021
Diophantine equationnumber theory

Problem Statement

Find all positive integers NN such that the following holds: There exist pairwise coprime positive integers a,b,ca,b,c with 1a+1b+1c=Na+b+c.\frac1a+\frac1b+\frac1c=\frac N{a+b+c}.
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