Integers of a quadratic field with prescribed sum and product

DOI10.4064/cm9023-11-2022OpenAlexW4322748201MaRDI QIDQ6086103

Gökhan Soydan, Andrew Bremner

Publication date: 9 November 2023

Published in: Colloquium Mathematicum (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4064/cm9023-11-2022

zbMATH Keywords

elliptic curvequadratic fieldChabauty methodDiophantine system

Mathematics Subject Classification ID

Quadratic extensions (11R11) Elliptic curves over global fields (11G05) Cubic and quartic Diophantine equations (11D25)

Cites Work

• The equation \(xyz=x+y+z=1\) in integers of a cubic field
• The Magma algebra system. I: The user language
• On a diophantine equation
• Sur le problème de M. Werner Mnich
• On unit solutions of the equation xyz = x+y+z in the ring of integers of a quadratic field
• The equation xyz=x+y+z=1 in integers of a quartic field
• Chabauty methods using elliptic curves
• On unit solutions of the equation xyz=x+y+z in a number field with unit group of rank 1
• Solutions to xyz = 1 and x+y+z = k in algebraic integers of small degree, I

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