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

Source: 2010 Romania District VII p2

September 1, 2024

number theoryalgebraInteger

Problem Statement

Let

x, y

be distinct positive integers. Show that the number

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

is not an integer.