Let $f$ be an entire function. State Cauchy's Integral Formula, relating the $n$th derivative of $f$ at a point $z$ with the values of $f$ on a circle around $z$.

State Liouville's Theorem, and deduce it from Cauchy's Integral Formula.

Let $f$ be an entire function, and suppose that for some $k$ we have that $|f(z)| \leqslant|z|^{k}$ for all $z$. Prove that $f$ is a polynomial.