JBMO-2012-4
- Tahmid Hasan
- Posts:665
- Joined:Thu Dec 09, 2010 5:34 pm
- Location:Khulna,Bangladesh.
Find all positive integers $x,y,z$ and $t$ such that $2^{x}3^{y}+5^{z}=7^{t}$
বড় ভালবাসি তোমায়,মা
- Phlembac Adib Hasan
- Posts:1016
- Joined:Tue Nov 22, 2011 7:49 pm
- Location:127.0.0.1
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Re: JBMO-2012-4
This problem offers you two options: either do huge calculations or use Zsigmondy's theorem. Though none of them is attractive, but, at my point of view, the first option is much more honorable.
My Solution:
Case:1 $x=1$
Case: 2 $x>1$
Case: $2.1$ $q=0$
Case: $2.2$ $q=y$
Here also two cases:
Case: $2.2.1$ $p=1$
Case: $2.2.2$ $x-p=1$
solution(s):
My Solution:
Here also two cases:
Case: $2.2.1$ $p=1$
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