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PAMO 2023 Problem 2

Source: 2023 Pan African Mathematics Olympiad Problem 2

May 17, 2023

PAMOnumber theory

Problem Statement

Find all positive integers

m

and

n

with no common divisor greater than 1 such that

m^3 + n^3

divides

m^2 + 20mn + n^2

. (Professor Yongjin Song)