Suppose a is an element of a group with |a| = m, and let n be...

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Suppose a is an element of a group with |a| = m, and let n be relatively prime to m. Show that then, a has an n-th root in the group, that is, a can be written as the n-th power of some element of the group. Suppose a is an element of a group with |a| = m, and let n be relatively prime to m. Show that then, a has an n-th root in the group, that is, a can be written as the n-th power of some element of the group.

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