Let's look at the two cases.
The first case is where n is prime.
When n is prime, φ(n) is equal to n - 1, so we're done.
We have exactly what we need for that from Fermat's Little Theorem.
Case two is where n is not prime, but we know that a and n are relatively prime.
In this case, we know since n is not prime,
there are some numbers that are not relatively prime to n.
Let's put those in a set. We'll call it R.
We're going to multiply that set by a mod n to get a new set we'll call S.
Now I have a quiz about R and S.
Here are the choices.
Check all of the statements that are true.
