BdMO Online Forum •India TST 2014

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India TST 2014

Posted: Thu Aug 25, 2016 12:51 pm

by RJHridi

Find all positive integers $x$, $y$ such that $x^{\ x + y}=y^ {3 x}$.

Re: India TST 2014

Posted: Sat Aug 27, 2016 12:00 pm

by Kazi_Zareer

Re: India TST 2014

Posted: Sat Aug 27, 2016 4:04 pm

by nahin munkar

Yeah , that's easy to see after some experiment. But u have to show your whole own solution.

Hint:

Re: India TST 2014

Posted: Sat Aug 27, 2016 8:07 pm

by Kazi_Zareer

nahin munkar wrote:Yeah , that's easy to see after some experiment. But u have to show your whole own solution.

Hint:
Use parity,divisibility (may be useful fact, $x$ & $y$ divides both sides),etc. And split it into cases.

It's easy to solve it. So I don't think to show whole solution. It can be solved easily by basics.