On Repdigits Which are Sums or Differences of Two k-Pell Numbers

IF 0.9 3区数学 Q2 MATHEMATICS

Mathematica Slovaca Pub Date : 2023-12-01 DOI:10.1515/ms-2023-0102

Mariama Ndao Faye, S. Rihane, A. Togbé

引用次数: 0

Abstract

ABSTRACT Let k ≥ 2. A generalization of the well-known Pell sequence is the k-Pell sequence whose first k terms are 0,…, 0, 1 and each term afterwards is given by the linear recurrence pn(k)=2Pn−1(k)+Pn−2(k)+⋯+Pn−k(k). The goal of this paper is to show that 11, 33, 55, 88 and 99 are all repdigits expressible as sum or difference of two k-Pell. The proof of our main theorem uses lower bounds for linear forms in logarithms of algebraic numbers and a modified version of Baker-Davenport reduction method (due to Dujella and Pethő). This extends a result of Bravo and Herrera [Repdigits in generalized Pell sequences, Arch. Math. (Brno) 56(4) (2020), 249–262].

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关于两个 k-Pell 数的和或差的重数

摘要设 k ≥ 2。众所周知的佩尔序列的广义化是 k-Pell 序列，其前 k 项为 0，...，0，1，之后的每项由线性递推公式 pn(k)=2Pn-1(k)+Pn-2(k)+⋯+Pn-k(k)给出。本文的目的是证明 11、33、55、88 和 99 都是可以用两个 k-Pell 的和或差来表示的重数字。我们主要定理的证明使用了代数数对数线性形式的下界，以及改进版的贝克-达文波特还原法（由杜杰拉和佩索提出）。这扩展了布拉沃和埃雷拉 [Repdigits in generalized Pell sequences, Arch.(Brno) 56(4) (2020), 249-262].

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematica Slovaca 数学-数学

CiteScore

2.10

自引率

6.20%

发文量

审稿时长

6-12 weeks

期刊介绍： Mathematica Slovaca, the oldest and best mathematical journal in Slovakia, was founded in 1951 at the Mathematical Institute of the Slovak Academy of Science, Bratislava. It covers practically all mathematical areas. As a respectful international mathematical journal, it publishes only highly nontrivial original articles with complete proofs by assuring a high quality reviewing process. Its reputation was approved by many outstanding mathematicians who already contributed to Math. Slovaca. It makes bridges among mathematics, physics, soft computing, cryptography, biology, economy, measuring, etc.　 The Journal publishes original articles with complete proofs. Besides short notes the journal publishes also surveys as well as some issues are focusing on a theme of current interest.