The 2-adic valuation of generalized Fibonacci sequences with an\n application to certain Diophantine equations

2017/02/19 by Bartosz Sobolewski, Sobolewski, Bartosz
Computer Science · Mathematics · Physics and Astronomy · #11B39 #11B65 #11D99 #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1702.05819

openalex publication_date 2017/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we focus on finding all the factorials expressible as a product\nof a fixed number of 2k-nacci numbers with k \≥ 2. We derive the 2-adic\nvaluation of the 2k-nacci sequence and use it to establish bounds on the\nsolutions of the initial equation. In addition, we specify a more general\nfamily of sequences, for which we can perform a similar procedure. We also\ninvestigate a possible connection of these results with p-regular sequences.\n

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