Question 120
Find the smallest positive integer $x_1$ such that $2006$ divides $x_{2006}$, if
$$
x_{n+1} = x_1^2 + x_2^2 + \dots + x_n^2 \text{ for each integer } n \ge 1.
$$
$$
x_{n+1} = x_1^2 + x_2^2 + \dots + x_n^2 \text{ for each integer } n \ge 1.
$$