This is a homework problem I have spent several hours on. A "hint" is given that we may use this fact: If $n,j,k \in \mathbb{N}$ satisfy $ n \geq 2$ and $1 \leq j+k \leq n$, then $n^2+j$ does not evenly divide $n^3+k$.
I cannot find any way to apply this fact. It leads me to believe I should use the string $0^{p^2}1^{p^3}$ or something like that, but I am really just not sure. The pumping lemma has given me trouble since the non regular language version.
Even small hints greatly appreciated at this point.