For a subset $\displaystyle S \subset \mathbb{N}$, let $\displaystyle S+S=\{s_1+s_2 : s_1,s_2 \in S\}$. Show that there is auniquepartition $\displaystyle A,B$ of $\displaystyle \mathbb{N}$ such that $\displaystyle A+A$ and $\displaystyle B+B$ contain no odd prime.