2004 AMC 12A Problem 25

For each integer n\geq 4, let a_n denote the base-n number 0.\overline{133}_n. The product a_4a_5...a_{99} can be expressed as \frac {m}{n!}, where m and n are positive integers and n is as small as possible. What is the value of m?

\text {(A) } 98 \qquad \text {(B) } 101 \qquad \text {(C) } 132\qquad \text {(D) } 798\qquad \text {(E) }962

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