MathNet 2012 Question 20

Let $a$, $b$, $c$, $d$ be integers with $a$, $c$ both nonzero, and define $x_n = \gcd(an + b, cn + d)$ for all positive integers $n$. Show that the sequence $x_1, x_2, x_3, \dots$ is unbounded if and only if $ad = bc$.