2007 Alabama ARML TST Problems/Problem 7

Problem

Find the number of distinct integers in the list

where $\lfloor x \rfloor$ represents the greatest integer less than or equal to $x$ .

The first time that the difference of two consecutive squares is greater than or equal to 2007 is $1004^2-1003^2=2007$ . Below $\left\lfloor \frac{1003^2}{2007}\right\rfloor =501$ , every non-negative integer can be reached. Then above that, each number is distinct. So there are $502+(2007-1004+1)=\boxed{1506}$ distinct integers in the given list.