Hello,

the task is to deduce theorem (2) from theorem (1):

(1) For cyclic group $\displaystyle C_n=<c>: \ ord(c^m)=\frac{n}{gcd(n,m)} \ , \ (m \in \mathbb{Z})$. Also $\displaystyle <c^m>=\{g^m|g \in C_n\}$.

(2) $\displaystyle \#\{g \in C_n|g^m=1\}=gcd(n,m)$

Group theory is fun, but in this case I can't get even started, though the puzzle seems trivial. I tried searching ProofWiki's group theory section for something useful, but I couldn't find anything. So, any help is welcome. Thank you.