BALTIC-WAY 2007 Problem 2

A sequence of integers $a_1,a_2,a_3,\ldots$ is called exact if $a_n^2-a_m^2=a_{n-m}a_{n+m}$ for any $n>m$ . Prove that there exists an exact sequence with $a_1=1,a_2=0$ and determine $a_{2007}$ .