# Math Help - Order Proof

1. ## Order Proof

If ord(a) = km, then ord(a^k) = m.

Can you show this proof? Thanks a lot!!!

2. Originally Posted by jzellt
If ord(a) = km, then ord(a^k) = m.

Can you show this proof? Thanks a lot!!!
Note that $(a^k)^m=e$ so that $|a^k|\mid m$, and if $(a^k)n=e\implies a^kn=e$ so that $kn\geqslant km\implies n\geqslant m$ so that $|a^k|\geqslant m$. But, this is only possible for positive numbers if $|a^k|=m$