## an element of a finite group

I need help with this theorum, please.

How is this (the attachment) true? It's for my cryptology class.

The rest of the day's notes are here: http://crypto.linuxism.com/thursday_december_13_2012
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 You might try applying Lagrange's theorem; that should set you in the right direction.

Recognitions:
 If $G$ is a finite group with order $|G|$ then for each element $a \in G$ , $a^{|G]} = I$, the identity.