期刊论文详细信息
Proceedings of the Japan Academy, Series A. Mathematical Sciences | |
Non-existence of certain Diophantine quadruples in rings of integers of pure cubic fields | |
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
【 预 览 】
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