Difference between revisions of "2017 USAJMO Problems/Problem 1"
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== Problem == | == Problem == | ||
| − | Prove that there are infinitely many pairs <math>(a,b)</math> such that <math>a^b+b^a</math> is divisible by <math>a+b</math>. | + | Prove that there are infinitely many distinct pairs <math>(a,b)</math> of relatively prime integers <math>a>1</math> and <math>b>1</math> such that <math>a^b+b^a</math> is divisible by <math>a+b</math>. |
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==Solution== | ==Solution== | ||
Revision as of 18:11, 19 April 2017
Problem
Prove that there are infinitely many distinct pairs 
of relatively prime integers 
and 
such that 
is divisible by 
.
Solution
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
See also
| 2017 USAJMO (Problems • Resources) | ||
| First Problem | Followed by Problem 2 | |
| 1 • 2 • 3 • 4 • 5 • 6 | ||
| All USAJMO Problems and Solutions | ||
