Let's say that we have the following problem:
Given an integer $n \geq 1$, find an irreducible polynomial $p(x,y) \in \mathbb C[x,y]$ such that $\deg p = n$.
I've heard the fact that there is an irreducible polynomial of every non-zero degree a couple of times. I'm interested in a short proof of that fact or a reference.
Also, is there a nice family of irreducible polynomials $p_n \in \mathbb C[x,y]$ such that $\deg p_n = n$?