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

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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
 
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Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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