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>.
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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 19:11, 19 April 2017

Problem

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

Solution

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See also

2017 USAJMO (ProblemsResources)
First Problem Followed by
Problem 2
1 2 3 4 5 6
All USAJMO Problems and Solutions
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