SOLUTIONS OF A GENERALIZED MARKOFF EQUATION IN FIBONACCI NUMBERS

被引：3
|
作者：
Hashim, Hayder Raheem [1 ]
Tengely, Szabolcs [1 ]
机构：
[1] Univ Debrecen, Inst Math, POB 400, H-4002 Debrecen, Hungary
来源：
MATHEMATICA SLOVACA | 2020年 / 70卷 / 05期
关键词：
Lucas sequences; Diophantine equations; Markoff equation;
D O I：
10.1515/ms-2017-0414
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we find all the solutions (X, Y, Z) = (F-I, F-J, F-K), where F-I, F-J, and F-K represent nonzero Fibonacci numbers, satisfying a generalization of Markoff equation called the Jin-Schmidt equation: AX(2) + BY2 + CZ(2) = DXYZ + 1. (C) 2020 Mathematical Institute Slovak Academy of Sciences
引用
收藏
页码：1069 / 1078
页数：10
相关论文
共 50 条
  • [31] AITKEN SEQUENCES AND GENERALIZED FIBONACCI NUMBERS
    MCCABE, JH
    PHILLIPS, GM
    MATHEMATICS OF COMPUTATION, 1985, 45 (172) : 553 - 558
  • [32] Generalized q-Fibonacci numbers
    Munarini, E
    FIBONACCI QUARTERLY, 2005, 43 (03): : 234 - 242
  • [33] On dual hyperbolic generalized Fibonacci numbers
    Soykan, Yuksel
    INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2021, 52 (01): : 62 - 78
  • [34] Generalized Fibonacci numbers and dimer statistics
    Lu, WT
    Wu, FY
    MODERN PHYSICS LETTERS B, 2002, 16 (30): : 1177 - 1181
  • [35] Generalized Fibonacci numbers and Dimer statistics
    Lu, WT
    Wu, FY
    PROCEEDINGS OF THE INTERNATIONAL SYMPOSIUM ON FRONTIERS OF SCIENCE, 2003, : 316 - 320
  • [36] A Binomial Sum of Generalized Fibonacci Numbers
    Plaza, Angel
    Smith, Jason L.
    Abel, Ulrich
    Bataille, Michel
    Boyadzhiev, Khristo N.
    Bradie, Brian
    Fedak, I. V.
    Fleischman, Dmitry
    Frontczak, Robert
    Ohtsuka, Hideyuki
    Schumacher, Raphael
    Stadler, Albert
    Terr, David
    FIBONACCI QUARTERLY, 2020, 58 (03): : 275 - 276
  • [37] Fibonacci Numbers of Generalized Zykov Sums
    Bautista-Ramos, Cesar
    Guillen-Galvan, Carlos
    JOURNAL OF INTEGER SEQUENCES, 2012, 15 (07)
  • [38] On the Solutions of Quaternion Difference Equations in Terms of Generalized Fibonacci-Type Numbers
    Gul, Kubra
    SYMMETRY-BASEL, 2022, 14 (10):
  • [39] COMBINATORIAL REPRESENTATION OF GENERALIZED FIBONACCI NUMBERS
    KLEIN, ST
    FIBONACCI QUARTERLY, 1991, 29 (02): : 124 - 131
  • [40] ON THE GENERALIZED k-FIBONACCI NUMBERS
    Falcon, Sergio
    MISKOLC MATHEMATICAL NOTES, 2021, 22 (01) : 193 - 199
12345