I have to write an essay about Fermat's theorem on sums of two squares. Now I found a proof in a book of the following theorem:
Let a prime number. Then the ideal is a prime ideal in if and only if .
Ok, now I have a question about the proof. The ideal in is a prime ideal if and only if the quotient ring is a integral domain (this is clear).
"Now there is a isomorphism and is a prime ideal in if and only if is irreducible in , which is equivalent that is no square mod ."
Is there a typing error? Is correct or should it be correctly ?
And what about " is no square mod "? I don't unterstand it.
Thanks in advance,