grandes-ecoles 2024 Q6

grandes-ecoles · France · x-ens-maths-d__mp Number Theory Algebraic Number Theory and Minimal Polynomials
Let $Q \in \mathbf{Q}[x]$ be a polynomial with rational coefficients whose constant term equals 1. Show that there exists an integer $b \geq 1$ such that $Q(bx)$ has integer coefficients.
Let $Q \in \mathbf{Q}[x]$ be a polynomial with rational coefficients whose constant term equals 1. Show that there exists an integer $b \geq 1$ such that $Q(bx)$ has integer coefficients.