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Take the gcd!

Source: Bulgaria JBMO TST 2023, Day 2, Problem 2

June 17, 2023
number theoryJBMO TSTgreatest common divisorDivisibility

Problem Statement

Determine the smallest positive integer n≥2n\geq 2 for which there exists a positive integer mm such that mnmn divides m2023+n2023+nm^{2023} + n^{2023} + n.
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