Question 33
Prove that, for any positive integers $d$ and $m$, a polynomial of degree $d$ with real coefficients cannot be expressed by a product of $m$ periodic functions. (A function $f: \mathbb{R} \to \mathbb{R}$ is called *periodic* if there exists a constant $T = T(f) \gt 0$ such that $f(x + T) = f(x)$ for all $x \in \mathbb{R}$.)