AT-OEMO-REG 2004 Problem 4

The sequence $< x_n >$ is defined through: $x_{n + 1} = \left(\frac {n}{2004} + \frac {1}{n}\right)x_n^2 - \frac {n^3}{2004} + 1$ for $n > 0$ Let $x_1$ be a non-negative integer smaller than $204$ so that all members of the sequence are non-negative integers. Show that there exist infinitely many prime numbers in this sequence.