Let http://alt1.artofproblemsolving.com/...ea377667b8.gif and http://alt2.artofproblemsolving.com/...bd49418f98.gif be positive integers and let the sequence http://alt2.artofproblemsolving.com/...fd0f8f56b2.gif be defined by http://alt1.artofproblemsolving.com/...6ebcf18b17.gif and http://alt1.artofproblemsolving.com/...774c64065a.gif for all non-negative integers http://alt2.artofproblemsolving.com/...00c274bdaa.gif. Prove that for any choice of http://alt1.artofproblemsolving.com/...ea377667b8.gif and http://alt2.artofproblemsolving.com/...bd49418f98.gif, the sequence http://alt1.artofproblemsolving.com/...26110acee0.gif contains infinitely many composite numbers.

How do I do this question? I just started self-learning number theory as recreation so yeah if anyone can show me how to solve it, I would really appreciate it.