x ^ y Mod z

[jemidiah]

Yup, the usual algorithm is exponentiation by squaring with modular reduction after each step, and I imagine better ones exist. It's a native command in Python if I remember correctly, so it's a common operation. Here's a Wikipedia section discussing it. You can write a recursive version of this algorithm extremely quickly, eg. using the pseudocode in the section following the one I linked and reducing the result each time before returning.

[bdbackify]

Thank you very much this was helpful the algorithm seems to be quick too. I was wondering if there's an even more generic algorithm for if y is a negative integer (in my case if it's negative it will always be -1).