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a nice problem for juniors

Source: Turkey Junior National Olympiad 2020 #P2

March 5, 2021
algebraInteger

Problem Statement

If the ratio 17m+43nm−n\frac{17m+43n}{m-n} is an integer where mm and nn positive integers, let's call (m,n)(m,n) is a special pair. How many numbers can be selected from 1,2,...,20211,2,..., 2021, any two of which do not form a special pair?
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