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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\qquad\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: [url=http://www.mathlinks.ro/Forum/viewtopic.php?t=61319]View all the problems from XIX Mexican Mathematical Olympiad

Problem Statement