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