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2018 PAMO Shortlist: Are there solutions to $4(ab - a - c^2) = b$?

Source: 2018 Pan-African Shortlist - N1

May 6, 2019
number theoryDiophantine equation

Problem Statement

Does there exist positive integers a,b,ca, b, c such that 4(ab−a−c2)=b4(ab - a - c^2) = b?
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