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.

引用

页码：37 / 46

页数：10

共 50 条

[1] Non-existence of certain Diophantine quadruples in rings of integers of pure cubic fields
Matic, Ljerka Jukic
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 2012, 88 (10) : 163 - 167
[2] Certifying Rings of Integers in Number Fields
Baanen, Anne
Villarello, Alain Chavarri
Dahmen, Sander R.
PROCEEDINGS OF THE 14TH ACM SIGPLAN INTERNATIONAL CONFERENCE ON CERTIFIED PROGRAMS AND PROOFS, CPP 2025, 2025, : 50 - 66
[3] Matrices as a diagonal quadratic form over rings of integers of certain quadratic number fields
Nullwala, Murtuza
Garge, Anuradha S.
LINEAR & MULTILINEAR ALGEBRA, 2024, 72 (12): : 2069 - 2089
[4] Rings of Integers in Number Fields and Root Lattices
Popov, V. L.
Zarhin, Yu. G.
DOKLADY MATHEMATICS, 2020, 101 (03) : 221 - 223
[5] Rings of Integers in Number Fields and Root Lattices
V. L. Popov
Yu. G. Zarhin
Doklady Mathematics, 2020, 101 : 221 - 223
[6] Monogenesis of the rings of integers in certain imaginary abelian fields
Shah, SIA
Nakahara, T
NAGOYA MATHEMATICAL JOURNAL, 2002, 168 : 85 - 92
[7] An arithmetic site for the rings of integers of algebraic number fields
Schmidt, A
INVENTIONES MATHEMATICAE, 1996, 123 (03) : 575 - 610
[8] On the 2-primary part of K-2 of rings of integers in certain quadratic number fields
Vazzana, A
ACTA ARITHMETICA, 1997, 80 (03) : 225 - 235
[9] ON ELEMENTARY ABELIAN 2-SYLOW K-2 OF RINGS OF INTEGERS OF CERTAIN QUADRATIC NUMBER-FIELDS
CONNER, PE
HURRELBRINK, J
ACTA ARITHMETICA, 1995, 73 (01) : 59 - 65
[10] TWO PROBLEMS CONCERNING IRREDUCIBLE ELEMENTS IN RINGS OF INTEGERS OF NUMBER FIELDS
Pollack, Paul
Troupe, Lee
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2017, 96 (01) : 44 - 58

← 1 2 3 4 5 →