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Ugly equation in integers!

Source: Iran TST 2012-Third exam-1st day-P3

May 15, 2012
number theory proposednumber theory

Problem Statement

Find all integer numbers xx and yy such that: (y3+xy−1)(x2+x−y)=(x3−xy+1)(y2+x−y).(y^3+xy-1)(x^2+x-y)=(x^3-xy+1)(y^2+x-y).
Proposed by Mahyar Sefidgaran
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