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b^2-4ac is not a perfect square

Source: Cono Sur Math Olympiad 2020 #2

December 3, 2020
number theorycombinatoricspigeonhole principle

Problem Statement

Given 20212021 distinct positive integers non divisible by 210102^{1010}, show that it's always possible to choose 33 of them aa, bb and cc, such that ∣b2−4ac∣|b^2-4ac| is not a perfect square.
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