1962 AHSME Problem 22

The number 121_b, written in the integral base b, is the square of an integer, for

\begin{array}{l} \textbf{(A)}\ b = 10,\text{ only} \qquad \textbf{(B)}\ b = 10 \text{ and } b = 5, \text{ only} \qquad \\ \textbf{(C)}\ 2\leq b\leq 10\qquad \textbf{(D)}\ b > 2\qquad \textbf{(E)}\ \text{no value of }b \end{array}

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