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Diophantine equation with HIGH values

Source: OMEC Ecuador National Olympiad Final Round 2021 N3 P6 day 2

November 8, 2024

number theoryDiophantine equation

Problem Statement

Find all positive integers

a, b, c

such that

ab+1

and

c

are coprimes and:

a(ba+1)(ca^2+ba+1)=2021^{2021}