## JBMO-2012-4

- Tahmid Hasan
**Posts:**665**Joined:**Thu Dec 09, 2010 5:34 pm**Location:**Khulna,Bangladesh.

### JBMO-2012-4

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:

Here also two cases:

solution(s):

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: $2.2.2$ $x-p=1$**Welcome to BdMO Online Forum. Check out Forum Guides & Rules