How do you write a program that solves unknowns?

[skace]

Hello, I would like to write a code that solves an expression with unknowns. How would I go about doing this? Any help would be appreciated. The puzzle is:
x^n + y^n = z^n
N > 2

Thanks

[ResidentBiscuit]

http://en.wikipedia.org/wiki/Fermat's_Last_Theorem