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

页数：27

共 30 条

[1]

[Anonymous], 1970, Analytic Inequalities

[2]

Apostol T. M., 1976, INTRO ANAL NUMBER TH

[3]

Baker A., 1972, Acta Arith, V21, P117, DOI DOI 10.4064/AA-21-1-117-129

[4]

BAKER A, 1977, TRANSCENDENCE THEORY, P1

[5]