Notations.

The set of non-negative integer numbers, integer numbers and rational numbers are denoted respectively ${\mathbb{N}}$ , ${\mathbb{Z}}$ and ${\mathbb{Q}}$ , as usual. For a ring ${\mathbb{A}}$ , we denote by ${\mbox{${\mathbb{A}}$}}[x]$ the ring of univariate polynomials in $x$ with coefficients in ${\mathbb{A}}$ .