Non-existence of certain Diophantine quadruples in rings of integers of pure cubic fields

DOI10.3792/pjaa.88.163zbMath1284.11057OpenAlexW1967479791MaRDI QIDQ1949172

Ljerka Jukić Matić

Publication date: 25 April 2013

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.pja/1354802414

zbMATH Keywords

cubic fieldsDiophantine quadruples

Mathematics Subject Classification ID

Quadratic and bilinear Diophantine equations (11D09) Congruences in many variables (11D79) Cubic and quartic extensions (11R16)

Related Items (1)

On a conjecture of Franušić and Jadrijević: counter-examples

Cites Work

• Diophantine quadruples in \(\mathbb {Z}[\sqrt {4k+3}\)]
• On \(k\)-triad sequences
• On differences of two squares in some quadratic fields
• A diophantine problem in ℤ[1 + \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} \(\sqrt d\) \end{document})/2]
• Sets in Which xy + k is Always a Square
• Generalization of a problem of Diophantus
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