1960 AHSME Problem 25

Let m and n be any two odd numbers, with n less than m. The largest integer which divides all possible numbers of the form m^2-n^2 is:

\textbf{(A)}\ 2\qquad \textbf{(B)}\ 4\qquad \textbf{(C)}\ 6\qquad \textbf{(D)}\ 8\qquad \textbf{(E)}\ 16

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