USAJMO/USAMO 2017 P1
USAJMO/USAMO 2017 P1
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 $a+b$.

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Re: USAJMO/USAMO 2017 P1
When $a,b$ € $N$ and it follows that $a^x$=$b^y$,there exists $t$ € $N$ such that $a$=$t^k$,$b$=$t^q$.This lemma can be quite handy in this problem.
 Atonu Roy Chowdhury
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 Location: Chittagong, Bangladesh
 Thanic Nur Samin
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Re: USAJMO/USAMO 2017 P1
Are you sure that helps? $a$ and $b$ need to be coprime.aritra barua wrote:When $a,b$ € $N$ and it follows that $a^x$=$b^y$,there exists $t$ € $N$ such that $a$=$t^k$,$b$=$t^q$.This lemma can be quite handy in this problem.
Hammer with tact.
Because destroying everything mindlessly isn't cool enough.
Because destroying everything mindlessly isn't cool enough.