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

Proceedings of the Japan Academy, Series A. Mathematical Sciences

article

Ljerka Jukić Matić¹ 

[1] Department of Mathematics, University of Osijek

关键词: Diophantine quadruples;    cubic fields.;   

DOI  :  10.3792/pjaa.88.163

学科分类：数学（综合）

来源: Japan Academy

【 摘 要 】

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.

【 授权许可】

Unknown