18. Find the largest positive integer $n$ such that $n+10$ is a divisor of $n^{3}+2011$.
18. Answer: 1001. $\frac{n^{3}+2011}{n+10}=n^{2}-10 n+100+\frac{1011}{n+10}$. This is an integer if and only if $(n+10) \mid 1011$. The maximum value of $n$ is $1011-10=1001$.