Originally Posted by

**strider2** I'm trying to figure this problem out and need a little help.

So suppose n is an integer and $\displaystyle a \in \mathbb{F}$ and suppose $\displaystyle a^n = 1$.

also $\displaystyle 0 < k<n$ and $\displaystyle k \mid n$. Prove that if $\displaystyle 0<k<n$ then $\displaystyle a^k \neq 1$.

So far my proof:

Suppose a contradiction.

Let $\displaystyle a^k =1$, then $\displaystyle gcd(k,n) = d$.

I write the linear combination $\displaystyle d = sk + tn$ for some integers t,n.

then $\displaystyle a^d = 1$

where do i go from here?