# Generator of Cyclic Group/Examples/C8

## Examples of Generators of Cyclic Groups

Let $C_8$ be generated by $x$:

$C_8 = \gen x$

The set of generators of the cyclic group $C_8$ is:

$\set {x, x^3, x^5, x^7}$

## Proof

From Power of Generator of Cyclic Group is Generator iff Power is Coprime with Order, $C_8$ is generated by any $x^n$ where $n \perp 8$.

Hence the result.

$\blacksquare$