When to use Fermat's Little Theorem and Euler's Generalization of Fermat's Little Theorem

Question

I guess I am having a lot of trouble doing questions and knowing that I have to use either one of these theorems. For a first year group theory/ring theory class what are some tell-tale hints for when to use either one of these theorems?

Answer 1

Fermat's little theorem applies only if $p$ is a prime, whereas the Euler-Fermat theorem can be used for any number. When in doubt, use the generalisation. (I could give a more specific answer if you gave some examples of problems where you don't know which theorem to use).