(a) Show that if $\alpha \in \mathbb { Q }$ is an algebraic integer, then $\alpha \in \mathbb { Z }$.\\
(b) Show that if $\alpha \in \mathbb { C }$ is an algebraic integer then $\Pi _ { \alpha } \in \mathbb { Z } [ X ]$.
Hint: use the theorem admitted in the introduction (the set of algebraic integers is a subring of $\mathbb{C}$) as well as question 5a.