If m is a primitive root mod n, prove that {$\displaystyle m,m^2,m^3,.......,m^\phi^(^n^)$}

runs through all numbers nod n that are relatively prime to n.

I assume it has something to do with $\displaystyle \phi(n) =$ numbers relatively prime to n

and the fact that it's a prim root it runs through all the numbers but not sure how to succinctly prove it.