For which prime numbers p is the quotient ring a field?
From theorems in my notes, I know this quotient ring is a field if is a maximal ideal, i.e is irreducible modulo p over the field .
I don't see where to go from here though.. any help would be great
so if p mod4 ... p must satisfy one of these:
p=0mod4 but this is not true as a prime number can't be divided by 4.
p=2mod4 but this is also not true as it would mean p is even.
Therefore, p=3mod4, in order for the quotient ring to be a field.
I think that's it
Thank you for your help! I would rep you if I could again