CR-MO 2010 Problem 2

Consider the sequence $x_n>0$ defined with the following recurrence relation:

$$x_1 = 0$$

and for $n>1$ $$(n+1)^2x_{n+1}^2 + (2^n+4)(n+1)x_{n+1}+ 2^{n+1}+2^{2n-2} = 9n^2x_n^2+36nx_n+32.$$

Show that if $n$ is a prime number larger or equal to $5$ , then $x_n$ is an integer.