The extensibility of the D(±k)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$D(\pm k)$$\end{document}-triple {k∓1,k,4k∓1}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{k\mp 1,k, 4k\mp 1\}$$\end{document}

被引：1
作者：
Appolinaire Dossavi-Yovo
Bo He
Alain Togbé
机构：
[1] Institut de Mathématiques et de Sciences Physiques,Department of Mathematics
[2] Institute of Mathematics,Department of Mathematics, Statistics, and Computer Science
[3] Aba Teachers University,undefined
[4] Hubei University for Nationalities,undefined
[5] Purdue University Northwest,undefined
来源：
Afrika Matematika | 2017年 / 28卷 / 3-4期
关键词：
Diophantine ; -tuple; Pell equation; Linear forms in logarithms; 11D09; 11D45; 11B37; 11J86;
D O I：
10.1007/s13370-016-0466-4
中图分类号：
学科分类号：
摘要：
In this paper, we consider the D(±k)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$D(\pm k)$$\end{document}-triple {k∓1,k,4k∓1}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{k\mp 1,k, 4k\mp 1\}$$\end{document} and we prove that, if k is not a perfect square then:There is no d such that {k-1,k,4k-1,d}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{k-1,k, 4k-1, d\}$$\end{document} is a D(k)-quadruple;If {k,k+1,4k+1,d}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{k,k+1,4k+1,d \}$$\end{document} is a D(-k)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$D(-k)$$\end{document}-quadruple, then d=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d=1$$\end{document}. This extends a work done by Fujita [13].
引用
收藏
页码：563 / 574
页数：11
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