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7th degree Diophantine

Source: 2017 USAJMO #2

April 19, 2017
AMCUSA(J)MOUSAJMO2017 USAJMODiophantine equation

Problem Statement

Consider the equation
(3x3+xy2)(x2y+3y3)=(xāˆ’y)7(3x^3+xy^2)(x^2y+3y^3)=(x-y)^7
(a) Prove that there are infinitely many pairs (x,y)(x,y) of positive integers satisfying the equation. (b) Describe all pairs (x,y)(x,y) of positive integers satisfying the equation.
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