If you find any mistakes, please make a comment! Thank you.

Compute multiplicative orders in Z/(36)

Find the orders of the following elements of the multiplicative group $(\mathbb{Z}/(36))^\times$: $\overline{1}$, $\overline{-1}$, $\overline{5}$, $\overline{13}$, $\overline{-13}$, and $\overline{17}$.


$\overline{n}$ Reasoning order
$\overline{1}$ 1
$\overline{-1}$ $\overline{-1} \cdot \overline{-1} = \overline{1}$ 2
$\overline{5}$ The powers of $\overline{5}$ are $\overline{5}$, $\overline{25}$, $\overline{17}$, $\overline{13}$, $\overline{29}$, and $\overline{1}$. 6
$\overline{13}$ The powers of $\overline{13}$ are $\overline{13}$, $\overline{25}$, and $\overline{1}$. 3
$\overline{-13}$ The powers of $\overline{-13}$ are $\overline{-13} = \overline{23}$, $\overline{25}$, $\overline{35}$, $\overline{13}$, $\overline{11}$, and $\overline{1}$. 6
$\overline{17}$ The square of $\overline{17}$ is $\overline{1}$. 2


This website is supposed to help you study Linear Algebras. Please only read these solutions after thinking about the problems carefully. Do not just copy these solutions.
Close Menu