33. What is the largest positive integer $n$ for which $n^{3}+2006$ is divisible by $n+26$ ?
33. Ans: 15544. $n^{3}+2006=(n+26)\left(n^{2}-26 n+676\right)-15570$. So if $n+26$ divides $n^{3}+2006, n+26$ must divide 15570 . Thus the largest $n$ is 15544 .