## USAJMO/USAMO 2017 P1

For discussing Olympiad Level Number Theory problems
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### 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 $a+b$.

aritra barua
Posts: 57
Joined: Sun Dec 11, 2016 2:01 pm

### 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
Posts: 63
Joined: Fri Aug 05, 2016 7:57 pm

### Re: USAJMO/USAMO 2017 P1

Quite easy as USAMO #1
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Thanic Nur Samin
Posts: 176
Joined: Sun Dec 01, 2013 11:02 am

### Re: USAJMO/USAMO 2017 P1

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.
Are you sure that helps? $a$ and $b$ need to be coprime.
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