Multiplicative order of a number

[koolkuzz]

I'm stuck on a question that requires me to prove the following:

Let s,n ∈ N, a ∈ Z and (a,n) = 1. (Note: a & n are coprime)
Prove that ord_na^s = ord_na implies that (s, ord_n a) = 1.

I have tried using Proof by contradiction, but seem to go nowhere with this.

Can you help?

 

[ystael]

Suppose $$(s, \mathop{\mathrm{ord}_n} a) = d$$ and put $$s = de$$. Observe that $$a^s = (a^d)^e$$. What is $$\mathop{\mathrm{ord}_n} a^d$$?