AHSME 1962 Problem 38

The population of Nosuch Junction at one time was a perfect square. Later, with an increase of $100$, the population was one more than a perfect square. Now, with an additional increase of $100$, the population is again a perfect square.

The original population is a multiple of: $\textbf{(A)}\ 3 \textbf{(B)}\ 7 \textbf{(C)}\ 9 \textbf{(D)}\ 11 \textbf{(E)}\ 17$