Doubly periodic function

Question

A function $f(z)$ on the complex plane is doubly periodic if there are two periods $\omega_{0}$ and $\omega_{1}$ of $f(z)$ that do not lie on the same line through to the origin (that is, $\omega_{0}$ and $\omega_{1}$ are linearly independent over the reals and $f(z+\omega_{0})=f(z+\omega_{1})=f(z)$ for all complex number $z$). Prove that the only entire functions that are doubly periodic are the constants.

Answer 1

Hint: show that they are bounded and apply Liouville