Equation with exponents

• Sep 17th 2011, 06:17 AM
gollum
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 :)
• Sep 17th 2011, 06:58 AM
Wilmer
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...
• Sep 17th 2011, 07:37 AM
gollum
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.
• Sep 17th 2011, 08:40 AM
islam
Re: Equation with exponents
r u sure there r not any more?
• Sep 17th 2011, 10:03 AM
Wilmer
Re: Equation with exponents
Quote:

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.