Hi!

I was wandering if anyone of you could help me solve the following equation:

$\displaystyle 2^x + 5^y = k^2$

where $\displaystyle x, y, k$ are integers.

I know the best way to solve it is to use modulo but, to be honest, I don't really know how modulo works in such equations.

Maybe you have another approach to this task - please share it

2. ## Re: Equation with exponents

Here's 2:
(2,1,3): 2^2 + 5^1 = 3^2

(3,0,3): 2^3 + 5^0 = 3^2

Perhaps someone else will have a "trick" for you...

3. ## Re: Equation with exponents

Thanks
I do hope someone will have a trick for me, because there needs to be a proof that there aren't any more solutions.

4. ## Re: Equation with exponents

r u sure there r not any more?

5. ## Re: Equation with exponents

Originally Posted by islam
r u sure there r not any more?
Well, I wrote short program to find these: contrary to what
I had asssumed, couldn't find any!
Why do you think there's more, islam? Got an example?
By the way, for your benefit, I suggest you start using
are (not r) and you (not u): may cause problems if you're
typing a math problem with variables.