The sequence <xn> is defined through:
x_{n \plus{} 1} \equal{} \left(\frac {n}{2004} \plus{} \frac {1}{n}\right)x_n^2 \minus{} \frac {n^3}{2004} \plus{} 1 for n>0
Let x1 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. inductionnumber theoryprime numbersalgebra unsolvedalgebra