Four consecutive integers have a product that is a perfect square. What are these numbers?
The product of four consecutive integers can also be written as follows:

$$
(n-1) n(n+1)(n+2)=n^{4}-n^{2}+2 n^{3}-2 n=\left(n^{2}+n-1\right)^{2}-1
$$

This is only a perfect square if $n^{2}+n-1= \pm 1$. This is precisely true if one of the original four numbers is 0.