$ c$ is a positive integer. Consider the following recursive sequence: $ a_1=c, a_{n+1}=ca_{n}+\sqrt{(c^2-1)(a_n^2-1)}$, for all $ n \in N$. Prove that all the terms of the sequence are positive integers.
Problem
Source: Prove that a sequence containts only integers
Tags: inequalities, algebra, polynomial, algebra proposed