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Math Help - Order Proof

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    Order Proof

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

    Can you show this proof? Thanks a lot!!!
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by jzellt View Post
    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
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