2017 USAJMO Problems/Problem 2
Problem:
Consider the equation
![\[\left(3x^3 + xy^2 \right) \left(x^2y + 3y^3 \right) = (x-y)^7.\]](http://latex.artofproblemsolving.com/5/1/5/5156a3323a4c2b47a971e779fb93769c35814611.png)
(a) Prove that there are infinitely many pairs 
of positive integers satisfying the equation.
(b) Describe all pairs of positive integers satisfying the equation.
Solution
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
See also
| 2017 USAJMO (Problems • Resources) | ||
| Preceded by Problem 1 |
Followed by Problem 3 | |
| 1 • 2 • 3 • 4 • 5 • 6 | ||
| All USAJMO Problems and Solutions | ||
