Multiplicative Dependent Pairs in the Sequence of Padovan Numbers

IF 0.9 3区数学 Q2 MATHEMATICS

Mathematica Slovaca Pub Date : 2023-10-01 DOI:10.1515/ms-2023-0083

Mitashree Behera, Prasanta Kumar Ray

引用次数: 0

Abstract

ABSTRACT The Padovan sequence { P n } n ≥0 is a ternary recurrent sequence defined recursively by the relation P n = P n –2 + P n –3 with initials P 0 = P 1 = P 2 = 1. In this note, we search all pairs of multiplicative dependent vectors whose coordinates are Padovan numbers. For this purpose, we apply Matveev’s theorem to find the lower bounds of the non-zero linear forms in logarithms. Techniques involving the LLL algorithm and the theory of continued fraction are utilized to reduce the bounds.

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帕多万数序列中的乘法相关对

帕多万序列{pn} n≥0是一个由pn = pn -2 + pn -3的关系递归定义的三元循环序列，首字母P 0 = p1 = p2 = 1。在本文中，我们搜索坐标为帕多万数的所有乘法相关向量对。为此，我们应用Matveev定理来求对数非零线性形式的下界。利用LLL算法和连分式理论来降低边界。

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.