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

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

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

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.