- Let $u$ a algebraic number. Prove that exists a natural number $n\in \mathbb{Z}$ such that $nu$ is a algebraic integer
- If $u$ is algebraic integer and $n\in \mathbb{Z}$ then $u+n$ and $nu$ are algebraic integers.
I don't see how can I start.
Remember that: $u$ is algebraic integer if it is a root by a monic polynomial $f(x)\in \mathbb{Z}[x]$.