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Expression in variables m and n divides other two

Source: Mexico National Olympiad Mock Exam 2019 P2

October 15, 2019
number theoryDivisibilityalgebra

Problem Statement

Find all pairs of positive integers (m,n)(m, n) such that m2āˆ’mn+n2+1m^2-mn+n^2+1 divides both numbers 3m+n+(m+n)!3^{m+n}+(m+n)! and 3m3+n3+m+n3^{m^3+n^3}+m+n.
Proposed by Dorlir Ahmeti
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