Question on algebraic integers.

Question

I'm currently studying algebraic extension and I found this problem: if $\alpha\in\mathbb{Q}$ is an algebraic integer prove $\alpha\in\mathbb{Z}$. So far I know from the definition that if $\alpha = \frac{a}{b}$ for $a,b\in\mathbb{Z}$ and $b\neq 0$ we can deduce $b^{n}\alpha$ is also an algebraic integer. I've couldn´t go any further.