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
These problems are copyrighted © by the Mathematical Association of America, as part of the 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 | ||
