1957 AHSME Problem 42

If S = i^n + i^{-n}, where i = \sqrt{-1} and n is an integer, then the total number of possible distinct values for S is:

\textbf{(A)}\ 1\qquad \textbf{(B)}\ 2\qquad \textbf{(C)}\ 3\qquad \textbf{(D)}\ 4\qquad \textbf{(E)}\ \text{more than 4}

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