Order of Group Element not less than Order of Power/Proof 1

Proof
Let $\left|{g}\right| = n$.

Then from Order of Power of Group Element:
 * $\forall m \in \Z: \left|{g^m}\right| = \dfrac n {\gcd \left\{{m, n}\right\}}$

where $\gcd \left\{{m, n}\right\}$ denotes the greatest common divisor of $m$ and $n$.

The result follows from Greatest Common Divisor is at least 1.