Recall that a perfect square is the square of some integer.  How many perfect squares less than 10,000 can be represented as the difference of two consecutive perfect squares?
I know that the difference of two consecutive perfect squares is always odd, because (n+1)^2 - n^2 = 2n + 1. So I need to find how many odd perfect squares are less. than 10,000. The largest odd perfect square less than 10,000 is 99^2, which is 9,801. The smallest odd perfect square is 1^2, which is 1. There are 50 of them. So there are 50 perfect squares less than 10,000 that can be represented as the difference of two consecutive perfect squares. 