lean_workbook_plus_61458

An alternative proof: Observe that the group of units $(\mathbb{Z}/d\mathbb{Z})^*$ is a subgroup of $(\mathbb{Z}/n\mathbb{Z})^*$ when $d | n$. Since the order of a subgroup divides the order of the group, $\varphi(d) | \varphi(n)$.