2017 USAMO Problems/Problem 1: Difference between revisions
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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>. | 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 18:28, 20 April 2017
Problem
Prove that there are infinitely many distinct pairs 
of relatively prime positive integers 
and 
such that 
is divisible by 
.
