Et $r = \zz[\sqrt{-n}]$ where $n$ is a squarefree integer $> 3$. prove that $2$, $\sqrt{-n}$, and $1 + \sqrt{-n}$ are all irreducible in $r$. \item prove that $r$ is not a ufd. [hint: show that either $\sqrt{-n}$ or $1+\sqrt{-n}$ is not prime.] \item find a non-principal ideal in r.