1956 AHSME Problem 36

If the sum 1 + 2 + 3 + \cdots + K is a perfect square N^2 and if N is less than 100, then the possible values for K are:

\textbf{(A)}\ \text{only }1\qquad \textbf{(B)}\ 1\text{ and }8\qquad \textbf{(C)}\ \text{only }8\qquad \textbf{(D)}\ 8\text{ and }49\qquad \textbf{(E)}\ 1,8,\text{ and }49

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