k-Fibonacci powers as sums of powers of some fixed primes

被引：0

作者：

Gomez, Carlos A. ^{[1
]}

Gomez, Jhonny C. ^{[5
]}

Luca, Florian ^{[2
,3
,4
]}

机构：

[1] Univ Valle, Dept Matemat, Calle 13 100-00, Cali 25360, Colombia

[2] Univ Witwatersrand, Sch Math, Johannesburg, South Africa

[3] King Abdulaziz Univ, Res Grp Algebra Struct & Applicat, Jeddah, Saudi Arabia

[4] UNAM, Ctr Ciencias Matemat, Morelia, Michoacan, Mexico

[5] Univ Libre Secc Pereira, Fac Ciencias Econom, Belmonte Ave Las Amer, Pereira, Colombia

来源：

MONATSHEFTE FUR MATHEMATIK | 2021年 / 195卷 / 01期

关键词：

k-generalized Fibonacci numbers; Linear forms in logarithms; Reduction methods; Prime powers;

D O I：

10.1007/s00605-021-01536-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let S = {p1,..., pt} be a fixed finite set of prime numbers listed in increasing order. In this paper, we prove that the Diophantine equation ( F (k) n)s = pa1 1 + ... + pat t, in integer unknowns n = 1, s = 1, k = 2 and ai = 0 for i = 1,..., t such that max {ai : 1 = i = t} = at has only finitely many effectively computable solutions. Here, F (k) n is the nth k-generalized Fibonacci number. We compute all these solutions when S = {2, 3, 5}. This paper extends the main results of [15] where the particular case k = 2 was treated.

引用

页码：73 / 105

页数：33

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