1972 AHSME Problem 31

When the number 2^{1000} is divided by 13, the remainder in the division is

\textbf{(A) }1\qquad \textbf{(B) }2\qquad \textbf{(C) }3\qquad \textbf{(D) }7\qquad \textbf{(E) }11

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