I've just spent past 5 days trying to get a solution to this:
Find all whole numbers, for whom the fraction
$\frac{n^3 + 2010}{n^2 + 2010}$
yields another whole number.
Before asking, please note that this is indeed an exercise from a math competition. However, this competition is already over, so don't worry; you're not doing my homework.
If anyone would be so kind to provide an explanation, could you formulate it in terms of high-school mathematics? Thanks.
P.S.: Please pardon my crude English. It's not my primary language.