On the $p$-adic valuation of third order linear recurrence sequences Article Swipe

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YOU? · · 2024 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2402.18279

In a recent paper, Bilu et al. studied a conjecture of Marques and Lengyel on the $p$-adic valuation of the Tribonacci sequence. In this article, we study the $p$-adic valuation of third order linear recurrence sequences by considering a generalisation of the conjecture of Marques and Lengyel for third order linear recurrence sequences. Suppose that $(x_n)$ is a third order linear recurrence sequence whose characteristic polynomial has a root $γ$ such that $|γ|>1$. We show that if there exists a prime $p$ for which the conjecture holds for $(x_n)$, then the solution set of the Diophantine equation given by $x_n=m!$ in positive integers $n,m$ is finite. We also show that the solutions can be effectively computed when the form of the conjecture is explicitly known.

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Valuation (finance) Order (exchange) Mathematics Third order Econometrics Combinatorics Economics Mathematical economics Applied mathematics Philosophy Theology Finance

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2402.18279
PDF: https://arxiv.org/pdf/2402.18279
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DOI: https://doi.org/10.48550/arxiv.2402.18279

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Title: On the $p$-adic valuation of third order linear recurrence sequences

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Language: en

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Publication year: 2024

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Publication date: 2024-02-28

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Authors: Deepa Antony, Rupam Barman

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Landing page: https://arxiv.org/abs/2402.18279

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Concepts: Valuation (finance), Order (exchange), Mathematics, Third order, Econometrics, Combinatorics, Economics, Mathematical economics, Applied mathematics, Philosophy, Theology, Finance

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