# Prove that an algebraic integer is a unit in Z(a)

1. Mar 7, 2013

### lahuxixi

I'm completely stuck here, can anyone help me?

2. Mar 7, 2013

### Dick

You shouldn't be completely stuck. One direction at least is easy. $\alpha^n+a_{n-1}\alpha^{n-1}+...+a_1 \alpha=-a_0$. Can you show that if $a_0=\pm 1$ then $\alpha$ is a unit?