# Difference between revisions of "2017 USAJMO Problems/Problem 2"

## Problem:

Consider the equation $$\left(3x^3 + xy^2 \right) \left(x^2y + 3y^3 \right) = (x-y)^7.$$

(a) Prove that there are infinitely many pairs $(x,y)$ of positive integers satisfying the equation.

(b) Describe all pairs $(x,y)$ of positive integers satisfying the equation.