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Simple diophantine equation

Source: 2021 2nd OMpD L2 P3 - Brazil - Olimpíada Matemáticos por Diversão

July 8, 2023
Diophantine equationnumber theory

Problem Statement

Determine all pairs of integer numbers (x,y)(x, y) such that: (x−y)2x+y=x−y+6\frac{(x - y)^2}{x + y} = x - y + 6
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