Difference between revisions of "2017 USAJMO Problems/Problem 2"
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==Problem:== | ==Problem:== | ||
| − | Prove that there are infinitely many | + | Consider the equation |
| + | <cmath>\left(3x^3 + xy^2 \right) \left(x^2y + 3y^3 \right) = (x-y)^7.</cmath> | ||
| + | |||
| + | (a) Prove that there are infinitely many pairs <math>(x,y)</math> of positive integers satisfying the equation. | ||
| + | |||
| + | (b) Describe all pairs <math>(x,y)</math> of positive integers satisfying the equation. | ||
==Solution== | ==Solution== | ||
Revision as of 19:12, 19 April 2017
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 | ||
