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(m^2 + n) and (n^2 + m) are both perfect squares

Source: Dutch NMO 1996 p2

January 29, 2020
Perfect SquaresPerfect Squarenumber theory

Problem Statement

Investigate whether for two positive integers mm and nn the numbers m2+nm^2 + n and n2+mn^2 + m can be both squares of integers.