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(x+y)^2/( x^3 + xy^2 - x^2y - y^3) not an integer

Source: 2011 Saudi Arabia Pre-TST November 2.3

January 1, 2022

number theoryInteger

Problem Statement

Let

x, y

be distinct positive integers. Prove that the number

\frac{(x+y)^2}{ x^3 + xy^2 - x^2y - y^3}

is not an integer