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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Originally Posted by MissMousey 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 $\displaystyle \text{gcd}$? what do you know about things with gcds?
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