Question 131
Let $f: \mathbb{R} \to \mathbb{R}$ and $g: \mathbb{R} \to \mathbb{R}$ be two quadratic functions with the following property: for any real number $r$, if $f(r)$ is an integer number, then $g(r)$ is also an integer number.
Prove that there are two integers $m$ and $n$ such that $g(x) = m f(x) + n$, for any real number $x$.
Prove that there are two integers $m$ and $n$ such that $g(x) = m f(x) + n$, for any real number $x$.