Q:

Prove that if $a$ and $a-1$ are relatively prime to $n$ then $1+a+a^2+\cdots+a^{\varphi(n)-1}\equiv 0 \pmod n$

I think I'm off to the right start where I applied Euler's Theorem and got:
$$a^{\varphi(n)}-(a-1)^{\varphi(n)}\equiv 0 \pmod n. $$
But I'm not sure how to proceed or if I have the right idea.

A:

Hint What is 
$$(1-a)(1+a+a^2+....+a^{\phi(n)-1})=?$$

