Number Theory

Let \(K\) be a number field and \(N:K\to {\mathbf{Z}}\) be its norm function.

• \(N(ab) = N(a)N(b)\)
• \(a\divides b \in K \implies N(a)\divides N(b)\in {\mathbf{Z}}\).
• \(a\in K^{\times}\iff N(a) = \pm 1\).