Additional Fact to a Homework Problem

Jeff Hevrin 03 Apr 2009 04:28

In one of our homeworks, we have to show that if a number is a primitive root mod(n), then its inverse is a primitive root as well.

In addition, I found online that, both a number and its inverse actually have the same order, too. We are actually just proving a certain case when the order is $\phi(n)$.

I won't give the proof of why it's true as it is a homework problem, but with some research it is true!