帕多万数序列中的乘法相关对

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

Mitashree Behera, Prasanta Kumar Ray

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引用次数: 0

摘要

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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Multiplicative Dependent Pairs in the Sequence of Padovan Numbers

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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