2017 USAJMO Problems/Problem 2

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 $a + b$ .

Solution

These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions.

2017 USAJMO (Problems • Resources)
Preceded by Problem 1	Followed by Problem 3
1 • 2 • 3 • 4 • 5 • 6
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2017 USAJMO Problems/Problem 2

Problem:

Solution

See also