Algebra Solutions: Compute multiplicative orders in ZZ/(n)

Find the orders of the following elements of the multiplicative group $(\mathbb{Z}/(12))^\times$ : $\overline{1}$ , $\overline{-1}$ , $\overline{5}$ , $\overline{7}$ , $\overline{-7}$ , $\overline{13}$ .

$\overline{n}$	Reasoning	$\|\overline{n}\|$
$\overline{1}$		1
$\overline{-1}$	$\overline{-1} \cdot \overline{-1} = \overline{1}$	2
$\overline{5}$	$\overline{5} \cdot \overline{5} = \overline{25} = \overline{1}$	2
$\overline{7}$	$\overline{7} \cdot \overline{7} = \overline{49} = \overline{1}$	2
$\overline{-7}$	$\overline{-7} = \overline{5}$	2
$\overline{13}$	$\overline{13} = \overline{1}$	1

Algebra Solutions

Compute multiplicative orders in ZZ/(n)

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