1961 AHSME Problem 4

Let the set consisting of the squares of the positive integers be called u; thus u is the set 1, 4, 9, 16 \ldots. If a certain operation on one or more members of the set always yields a member of the set, we say that the set is closed under that operation. Then u is closed under:

\begin{array}{l} \textbf{(A)}\ \text{Addition}\qquad \textbf{(B)}\ \text{Multiplication} \qquad \textbf{(C)}\ \text{Division} \qquad\\ \textbf{(D)}\ \text{Extraction of a positive integral root}\qquad \textbf{(E)}\ \text{None of these} \end{array}

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