ON D(w)-QUADRUPLES IN THE RINGS OF INTEGERS OF CERTAIN PURE NUMBER FIELDS

被引：0
|
作者：
Matic, Ljerka Jukic [1 ]
机构：
[1] Univ Osijek, Dept Math, Osijek 31000, Croatia
来源：
GLASNIK MATEMATICKI | 2014年 / 49卷 / 01期
关键词：
Diophantine quadruples; pure number fields; cyclic bases; DIOPHANTINE QUADRUPLES; POLYNOMIAL VARIANT;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The purpose of this paper is to show the non-existence of D(w)-quadruples in number fields of odd degree whose rings of integers are of the special form. We derive some elements which can not be represented as difference of squares in such rings and comment the non-existence of corresponding Diophantine quadruples. This relies on the non-solvability of system of congruences which we prove in some low-degree cases.
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页码：37 / 46
页数：10
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