The question I've encountered reading a textbook is as follows:
Show that if $n \in \mathbb{Z}_+$ and $a, b\in\mathbb{Z}$ have $(a,n)=(b,n) = (\mathrm{ord}_na,\mathrm{ord}_nb)=1$ then $\mathrm{ord}_n(ab) = (\mathrm{ord}_na)(\mathrm{ord}_nb)$
I appreciate any help. Thanks.