Algebraic Number Theory 24: Discriminants of Number Fields

In this lecture we prove two important facts about the discriminant of a number field. One determines the sign in terms of the arithmetic of the field. The other, Stickelberger's Theorem, says that the discriminant is either 1 or 0 modulo 4. These results can be found in section 2.9 of Milne's notes.

[christianharriviktorreibol]

How do we know the statement around 11.40 is true?