OMM 2005 Problem 3

Already the complete problem:

Determine all pairs $(a,b)$ of integers different from $0$ for which it is possible to find a positive integer $x$ and an integer $y$ such that $x$ is relatively prime to $b$ and in the following list there is an infinity of integers:

$\rightarrow \frac{a + xy}{b}$ , $\frac{a + xy^2}{b^2}$ , $\frac{a + xy^3}{b^3}$ , $\ldots$ , $\frac{a + xy^n}{b^n}$ , $\ldots$

One idea?

:arrow: View all the problems from XIX Mexican Mathematical Olympiad