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Characterization of geometric progressions of length 3 between 2004² and 2005²

Source:

November 28, 2019
inequalitiesgeometric sequencenumber theory

Problem Statement

Find all triples (x,y,z) (x,y,z) of natural numbers that are in geometric progression and verify the inequalities 4016016x<y<z4020025. 4016016\le x<y<z\le 4020025.