2006 AMC 10B Problem 18

Let a_1 , a_2 , ... be a sequence for which

a_1=2 , a_2=3, and a_n=\frac{a_{n-1}}{a_{n-2}} for each positive integer n \ge 3.

What is a_{2006}?

\mathrm{(A) \ } \frac{1}{2}\qquad \mathrm{(B) \ } \frac{2}{3}\qquad \mathrm{(C) \ } \frac{3}{2}\qquad \mathrm{(D) \ } 2\qquad \mathrm{(E) \ } 3

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