Easy# Number of Cyclic Subgroups, Reduced Residues

ABSALG-KN10XE

Let $G$ be a group. The order of $G$ is the number of elements in the set $G$.

The cyclic subgroups of $G$ are the subgroups equal to:

$\langle g\rangle:=\{g^n\mid n\in{\mathbb Z}\}$ (multiplicative notation)

...for some $g\in G$.

Let $({\mathbb Z}/m{\mathbb Z})^\ast$ denote the group of residue classes mod $m$ of the integers coprime to $m$ (i.e. the reduced residues).

**Which of the following is TRUE?**