Question 106
Let $a$, $b$ be relatively prime integers. Sequence $(x_n)_{n=1}^{\infty}$ of natural numbers is constructed in such a way that for each $n \gt 1$ applies $x_n = a x_{n-1} + b$. Prove that in any such sequence every entry $x_n$ with index $n \gt 1$ divides infinitely many of other entries. Does this assertion hold for $n = 1$?