# Math Help - Units in Z20

1. ## Units in Z20

Make a list of units in Z20 and verify that they all map to units in Z4. Show that ther is a non-unit in Z20 that maps to a unit in Z4.

Thanks in advance for any help

2. Originally Posted by jzellt
Make a list of units in Z20 and verify that they all map to units in Z4. Show that ther is a non-unit in Z20 that maps to a unit in Z4.

$a\in\mathbb{Z}/20\mathbb{Z}$ is a unit $\iff (a,20)=1$.
Therefore the group of units of $\mathbb{Z}/20\mathbb{Z}$ is $\left(\mathbb{Z}/20\mathbb{Z}\right)^\times = \{1,3,7,9,11,13,17,19\}$.
$\left(\mathbb{Z}/4\mathbb{Z}\right)^\times = \{1,3\}$.