Let $l$ be an odd prime number and $\zeta$ be a primitive $l$-th root of unity in $\mathbb{C}$. Let $\mathbb{Q}(\zeta)$ be the cyclotomic field. Let $A$ be the ring of algebraic integers of $\mathbb{Q}(\zeta)$. Let $\alpha \in A$. Let $N(\alpha)$ be the norm of $\alpha$.
My question: How can we prove that $N(\alpha) \equiv 0$ or $\equiv 1$ (mod $l$)?