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Math Help - Prove that a^k has and order m/d

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    Prove that a^k has and order m/d

    Suppose that a is an element of order m in a group G, and k is an integer. If d = (k, m), prove that a^k has order m/d.

    So let k = dp for some integer p.

    To be edited.
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by MissMousey View Post
    Suppose that a is an element of order m in a group G, and k is an integer. If d = (k, m), prove that a^k has order m/d.

    So let k = dp for some integer p.

    To be edited.
    What do you think? I mean, what is the significance of the \text{gcd}? what do you know about things with gcds?
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