Markoff-Rosenberger triples in geometric progression
Enrique Gonz\'alez-Jim\'enez
TL;DR
This paper investigates solutions to the Markoff-Rosenberger equation where the solutions form a geometric progression within the ring of integers of a number field, expanding understanding of these special solutions.
Contribution
It introduces a study of Markoff-Rosenberger solutions constrained to geometric progressions in algebraic integer rings, a novel focus in the field.
Findings
Characterization of solutions in specific number fields
Conditions for solutions to form geometric progressions
Examples of solutions in various algebraic settings
Abstract
Solutions of the Markoff-Rosenberger equation ax^2+by^2+cz^2 = dxyz such that their coordinates belong to the ring of integers of a number field and form a geometric progression are studied.
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