Integers represented by Lucas sequences

被引：0
|
作者：
Hajdu, Lajos [1 ,2 ]
Tijdeman, Rob [3 ]
机构：
[1] Univ Debrecen, Inst Math, POB 400, H-4002 Debrecen, Hungary
[2] HUN REN Equat Funct Curves & Their Applicat Res Gr, Debrecen, Hungary
[3] Leiden Univ, Math Inst, Postbus 9512, NL-2300 RA Leiden, Netherlands
来源：
RAMANUJAN JOURNAL | 2025年 / 66卷 / 04期
关键词：
Lucas sequences; Integers represented by forms; Fibonacci polynomials; LOGARITHMS; DIVISORS; FORMS; TERM;
D O I：
10.1007/s11139-025-01041-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study the sets of integers which are n-th terms of Lucas sequences. We establish lower- and upper bounds for the size of these sets. These bounds are sharp for n sufficiently large. We also develop bounds on the growth order of the terms of Lucas sequences that are independent of the parameters of the sequence, which is a new feature.
引用
收藏
页数：27
相关论文
共 50 条
  • [31] On the discriminator of Lucas sequences
    Bernadette Faye
    Florian Luca
    Pieter Moree
    Annales mathématiques du Québec, 2019, 43 : 51 - 71
  • [32] GENERALIZED LUCAS SEQUENCES
    HOGGATT, VE
    BICKNELLJOHNSON, M
    FIBONACCI QUARTERLY, 1977, 15 (02): : 131 - 139
  • [33] ON PRIMES IN LUCAS SEQUENCES
    Somer, Lawrence
    Krizek, Michal
    FIBONACCI QUARTERLY, 2015, 53 (01): : 2 - 23
  • [34] A set of Lucas sequences
    Atanassov, Krassimir T.
    NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS, 2014, 20 (02) : 1 - 5
  • [35] Number of integers represented by families of binary forms (I)
    Fouvry, Etienne
    Waldschmidt, Michel
    ACTA ARITHMETICA, 2023, 209 (01) : 219 - 268
  • [36] Eligible integers represented by positive ternary quadratic forms
    Lu, Wei
    Qin, Hourong
    ACTA ARITHMETICA, 2017, 179 (01) : 17 - 23
  • [37] Notes on the (s, t)-Lucas and Lucas Matrix Sequences
    Civciv, Haci
    Turkmen, Ramazan
    ARS COMBINATORIA, 2008, 89 : 271 - 285
  • [38] On the number of integers represented by systems of Abelian norm forms
    Blomer, Valentin
    Schlage-Puchta, Jan-Christoph
    ACTA ARITHMETICA, 2006, 123 (02) : 183 - 199
  • [39] On the integers represented by x4-y4
    Dabrowski, Andrzej
    BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2007, 76 (01) : 133 - 136
  • [40] SQUAREFREE INTEGERS IN NONLINEAR SEQUENCES
    ROESLER, F
    PACIFIC JOURNAL OF MATHEMATICS, 1986, 123 (01) : 223 - 225
12345