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(x^2y + x) is a multiple of (xy^2 + 7) , find positive integers x,y

Source: KJMO 2014 p5

May 2, 2019
number theorymultiplepositive integersdivisible

Problem Statement

For positive integers x,yx,y, find all pairs (x,y)(x,y) such that x2y+xx^2y + x is a multiple of xy2+7xy^2 + 7.
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