Let $\displaystyle G$ be a cyclic groups. (Exist $\displaystyle x\in G $ so that $\displaystyle G=<x>={x^n:n\in \mathbb{Z}$)

Show that if $\displaystyle ord(x)=n$ then the number of genereted elements of $\displaystyle <x>$ is $\displaystyle \phi(n)$.