2005 Cayley Problem 25

The positive integers a, b and c satisfy \frac{1}{a^2} + \frac{1}{b^2} = \frac{1}{c^2}.

The sum of all possible values of a \le 100 is

\textbf{(A)}\ 315\quad \textbf{(B)}\ 615\quad \textbf{(C)}\ 680\quad \textbf{(D)}\ 555\quad \textbf{(E)}\ 620

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.