AMC 12B 2006 Problem 25

A sequence a_{1}, a_{2}, \ldots of non-negative integers is defined by the rule a_{n+2}= \left|a_{n+1}-a_{n}\right| for n \geq 1. If a_{1}=999, a_{2}<999, and a_{2006}=1, how many different values of a_{2} are possible?

Answer Choices
A. 165
B. 324
C. 495
D. 499
E. 660