2007 AMC 10A Problem 23

How many ordered pairs (m,n) of positive integers, with m \ge n, have the property that their squares differ by 96?

\text{(A)}\ 3 \qquad \text{(B)}\ 4 \qquad \text{(C)}\ 6 \qquad \text{(D)}\ 9 \qquad \text{(E)}\ 12

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.