1970 AHSME Problem 4

Let S be the set of all numbers which are the sum of the squares of three consecutive integers. Then we can say that:

\begin{array}{l} \textbf{(A) }\text{No member of }S\text{ is divisible by }2\qquad\\ \textbf{(B) }\text{No member of }S\text{ is divisible by }3\text{ but some member is divisible by }11\qquad\\ \textbf{(C) }\text{No member of }S\text{ is divisible by }3\text{ or }5\qquad\\ \textbf{(D) }\text{No member of }S\text{ is divisible by }3\text{ or }7\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.