.What is the remainder when dividing 38^213 by 13?

[talolard]

Homework Statement

Find the remainder when dividing $$38^{213}$$ by 13.

Homework Equations

Fermats little theorem: $$a^{p-1}\equiv 1 Mod(p)$$

The Attempt at a Solution

I tried proving this with fermats little theorem or using the more general Euler theorem but I am overlooking some manipulation. To my dismay 12 does not divide 213 and I am not seeing how to put the question in the right form. ANy help is greatly apreciarted.
Tal

 

[talolard]

Solved. Please erase