Show that this entire function is polynomial. Let $f$ be an entire function such that $ |f(z)| \to \infty$ as $|z| \to \infty$. Prove that $f$ is a polynomial.

Hint: The set of zeroes of $f$ is bounded and discrete, hence finite and this allows us to find a polynomial $p$ such that $f(z)=p(z)g(z)$ for some entire function $g\colon \mathbb C\to\mathbb C^\times$. What scenarios can happen with $g(z)$ as $z\to\infty$?
