Bounds on the number of squares in recurrence sequences

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Number Theory Pub Date : 2024-06-25 DOI:10.1016/j.jnt.2024.05.002

Paul M. Voutier

引用次数: 0

Abstract

We investigate the number of squares in a very broad family of binary recurrence sequences with $u_{0} = 1$ . We show that there are at most two distinct squares in such sequences (the best possible result), except under very special conditions where we prove there are at most three such squares.

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递推序列中方格数的界限

我们研究了一个非常广泛的二元递推序列家族中的方格数，该序列的....我们证明在这些序列中最多有两个不同的正方形（这是最好的结果），除非在非常特殊的条件下，我们证明最多有三个这样的正方形。

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

Journal of Number Theory 数学-数学

CiteScore

1.30

自引率

14.30%

发文量

122

审稿时长

16 weeks

期刊介绍： The Journal of Number Theory (JNT) features selected research articles that represent the broad spectrum of interest in contemporary number theory and allied areas. A valuable resource for mathematicians, the journal provides an international forum for the publication of original research in this field. The Journal of Number Theory is encouraging submissions of quality, long articles where most or all of the technical details are included. The journal now considers and welcomes also papers in Computational Number Theory. Starting in May 2019, JNT will have a new format with 3 sections: JNT Prime targets (possibly very long with complete proofs) high impact papers. Articles published in this section will be granted 1 year promotional open access. JNT General Section is for shorter papers. We particularly encourage submission from junior researchers. Every attempt will be made to expedite the review process for such submissions. Computational JNT . This section aims to provide a forum to disseminate contributions which make significant use of computer calculations to derive novel number theoretic results. There will be an online repository where supplementary codes and data can be stored.