Here is a simplified idea of what I am working to solve. I am unsure where to start (besides what I've listed below from looking at previous sections), or where to go from there. Thanks in advance for any help with this proof!

The Euler phi function ϕ gives the number of positive integers less than or equal to, and relatively prime to, a give positive integer. e.g. ϕ(3)=2, ϕ(5)=4. There is a generalization of Fermat's Little Theorem due to Euler:

Theorem.Let n be a positive integer and a∈ℤ with gcd(a,n)=1. Then a^(ϕ(n))≡1(mod n)

(a)Prove this theorem.

(b)Explain why Fermat's Little Theorem is a special case of this theorem.

What I've deduced so far.The fact that a^|G|=e for every a∈G, if G is finite with identity e, seems as if it will help.

LaGrange's Theorem and/or cosets will likely be used as well.

Thanks in advance. Any help/solution to this would be a lifesaver!