AHSME 1951 Problem 15

The largest number by which the expression $n^3 - n$ is divisible for all possible integral values of $n$, is: $\textbf{(A)}\ 2 \textbf{(B)}\ 3 \textbf{(C)}\ 4 \textbf{(D)}\ 5 \textbf{(E)}\ 6$