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Infinitely many solutions to floor equation

Source: Latvia BW TST 2021 P14

September 26, 2021
number theoryfloor function

Problem Statement

Prove that there exist infinitely many triples of positive integers (a,b,c)(a,b,c) so that a,b,ca,b,c are pairwise coprime and ⌊a22021⌋+⌊b22021⌋=⌊c22021⌋.\bigg \lfloor \frac{a^2}{2021} \bigg \rfloor + \bigg \lfloor \frac{b^2}{2021} \bigg \rfloor = \bigg \lfloor \frac{c^2}{2021} \bigg \rfloor.
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