1978 AHSME Problem 14

If an integer n > 8 is a solution of the equation x^2 - ax+b=0 and the representation of a in the base-n number system is 18, then the base-n representation of b is

\textbf{(A)}\ 18 \qquad \textbf{(B)}\ 20 \qquad \textbf{(C)}\ 80 \qquad \textbf{(D)}\ 81 \qquad \textbf{(E)}\ 280

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