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(x + y + 1) | 2xy and (x + y - 1) | (x^2 + y^2 - 1) , diophantine system

Source: Dutch IMO TST2 2012 p3

January 10, 2020
Diophantine Equationsdiophantinenumber theory

Problem Statement

Determine all pairs (x,y)(x, y) of positive integers satisfying x+y+1∣2xyx + y + 1 | 2xy and x+y−1∣x2+y2−1 x + y - 1 | x^2 + y^2 - 1.
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