India TST 2014

For discussing Olympiad Level Number Theory problems
RJHridi
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India TST 2014

Unread post by RJHridi » Thu Aug 25, 2016 12:51 pm

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

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Kazi_Zareer
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Location: Malibagh,Dhaka-1217

Re: India TST 2014

Unread post by Kazi_Zareer » Sat Aug 27, 2016 12:00 pm

$(1,1), (2,4), (5,25)$
Last edited by Kazi_Zareer on Sat Aug 27, 2016 8:09 pm, edited 2 times in total.
We cannot solve our problems with the same thinking we used when we create them.

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nahin munkar
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Re: India TST 2014

Unread post by nahin munkar » Sat Aug 27, 2016 4:04 pm

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.
Last edited by nahin munkar on Sun Aug 28, 2016 9:45 am, edited 1 time in total.
# Mathematicians stand on each other's shoulders. ~ Carl Friedrich Gauss

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Kazi_Zareer
Posts: 86
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Location: Malibagh,Dhaka-1217

Re: India TST 2014

Unread post by Kazi_Zareer » Sat Aug 27, 2016 8:07 pm

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.
We cannot solve our problems with the same thinking we used when we create them.

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