SAUDI ARABIAN MATHEMATICAL COMPETITIONS

First, we prove 2 lemmas as the problem in Level 4's Test. Then turn to the problem, since $P\left(\sqrt[3]{n^2}+\sqrt[3]{n}\right)=2016n+20\sqrt[3]{n^2}+16\sqrt[3]{n}$, then by the second lemma, we obtain $n-1\mid 20-16=4$. That is, $n\in \{5,3,2,0,-1,-3\}$, and we can easily check that these numbers satisfy the condition of the problem. $\square$