Question 111
Let $a$, $b$, $c$, $d$ be positive integers such that $ad \neq bc$ and $\text{gcd}(a, b, c, d) = 1$. Prove that, as $n$ runs through the positive integers, the values $\text{gcd}(an + b, cn + d)$ may achieve form the set of all positive divisors of some integer.