Difference between revisions of "2017 USAMO Problems/Problem 1"

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== Problem ==
 
== Problem ==
  
Prove that there are infinitely many distinct pairs <math>(a,b)</math> of relatively prime positive integers a>1 and b>1 such that <math>a^b+b^a</math> is divisible by <math>a+b</math>.
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Prove that there are infinitely many distinct pairs <math>(a,b)</math> of relatively prime positive 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>.

Revision as of 19:28, 20 April 2017

Problem

Prove that there are infinitely many distinct pairs $(a,b)$ of relatively prime positive integers $a>1$ and $b>1$ such that $a^b+b^a$ is divisible by $a+b$.