1. ## Group isomorphism

Show $\mathbb{Z}_{14}^* \cong \mathbb{Z}_{18}^*$.

2. $
\mathbb{Z}_{14} ^ \times
$
and $
\mathbb{Z}_{18} ^ \times
$
have the same order and both are cyclic, hence they are isomorphic.

(Remember that if $p>2$ is prime then $
\mathbb{Z}_{2p^k } ^ \times

$
is cyclic for all $k\in \mathbb{Z}^+$, to see this, read about primitive roots)