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December 2012 Non-existence of certain Diophantine quadruples in rings of integers of pure cubic fields
Ljerka Jukić Matić
Proc. Japan Acad. Ser. A Math. Sci. 88(10): 163-167 (December 2012). DOI: 10.3792/pjaa.88.163

Abstract

In this paper we derive some elements of the rings of integers in the cubic fields of the form $\mathbf{Q}(\sqrt[3]{d})$, where $d$ is even, which cannot be written as a difference of two squares in the considered ring. We show that corresponding Diophantine quadruples do not exist for such elements, what supports the hypothesis mainly proved for the ring of integers and for certain quadratic fields.

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Ljerka Jukić Matić. "Non-existence of certain Diophantine quadruples in rings of integers of pure cubic fields." Proc. Japan Acad. Ser. A Math. Sci. 88 (10) 163 - 167, December 2012. https://doi.org/10.3792/pjaa.88.163

Information

Published: December 2012
First available in Project Euclid: 6 December 2012

zbMATH: 1284.11057
MathSciNet: MR3004232
Digital Object Identifier: 10.3792/pjaa.88.163

Subjects:
Primary: 11D09, 11R16
Secondary: 11D79

Rights: Copyright © 2012 The Japan Academy

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Vol.88 • No. 10 • December 2012
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