I think they are expecting you to calculate the value from the definition of .
How many numbers below 2p are coprime to 2?
How many numbers below 2p are coprime to p?
So I was given a pretty easy problem
Calculate where is prime.
Which I can solve with what I have read online:
* Given if , then
Then it's pretty easy:
and since , then
But the problem is, in class we haven't proved * ,so we can't use it. Pretty much all we know about is that it is the number of positive integers wich are less than m and relatively prime to m. AND .
I'm just wondering how I would go about doing this?
Thanks
EDIT:
After some thought and more reading I came to this:
CASE 1 : if p != 2
Case 2:
Am I correct in my reasoning?