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Find the right way to work with modulo

Source: Science ON 2021 grade VIII/1

March 8, 2021
number theorymodular arithmeticabstract algebra

Problem Statement

Are there any integers a,ba,b and cc, not all of them 00, such that a2=2021b2+2022c2  ?a^2=2021b^2+2022c^2~~?
(Cosmin Gavrilă)
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