2006 AMC 12B Problem 25

A sequence a_1,a_2,\ldots of non-negative integers is defined by the rule a_{n+2}=|a_{n+1}-a_n| for n\geq 1. If a_1=999, a_2<999 and a_{2006}=1, how many different values of a_2 are possible?

\mathrm{(A)}\ 165 \qquad \mathrm{(B)}\ 324 \qquad \mathrm{(C)}\ 495 \qquad \mathrm{(D)}\ 499 \qquad \mathrm{(E)}\ 660

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