# Prove that a^k has and order m/d

• May 2nd 2010, 02:05 PM
MissMousey
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.
• May 2nd 2010, 09:59 PM
Drexel28
Quote:

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 $\text{gcd}$? what do you know about things with gcds?