Sincere thanks to readers who have completed the Free Personality Quiz!
Today we will revise some basic Group Theory. Let be a group and . Assume that has finite order . Find the order of where is an integer.
Answer: , where .
Our strategy is to prove that is the least smallest integer such that .
Now, we have . Note that is an integer and thus a valid power.
Suppose to the contrary there exists such that .
Since has finite order , we have , which leads to . Note that and are relatively prime.
Thus , which implies that which is a contradiction. This proves our result. 🙂