[Math] Determining the number of elements of order $n$ in a finite group which has $k$ cyclic subgroups of order $n$.

Question

Let $n,k$ be positive integers and let $G$ be a group which has $k$ cyclic subgroups of order $n$. Determine with proof the number of elements of order $n$ in $G$.

For example, a finite group $G$ which has $28$ cyclic subgroups of order $4$ has $56$ elements of order $4$.

Thanks so much for taking your time!

Answer 1

Hint: In any cyclic subgroup of order $n$, there are $\varphi(n)$ generators.