On prime powers in linear recurrence sequences

In this paper we consider the Diophantine equation [Formula: see text] where [Formula: see text] is a linear recurrence sequence, p is a prime number, and x is a positive integer. Under some technical hypotheses on [Formula: see text] , we show that, for any p outside of an effectively computable fi...

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Detalles Bibliográficos
Autores principales: Odjoumani, Japhet, Ziegler, Volker
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2021
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10540468/
https://www.ncbi.nlm.nih.gov/pubmed/37780137
http://dx.doi.org/10.1007/s40316-021-00163-9
Descripción
Sumario:In this paper we consider the Diophantine equation [Formula: see text] where [Formula: see text] is a linear recurrence sequence, p is a prime number, and x is a positive integer. Under some technical hypotheses on [Formula: see text] , we show that, for any p outside of an effectively computable finite set of prime numbers, there exists at most one solution (n, x) to that Diophantine equation. We compute this exceptional set for the Tribonacci sequence and for the Lucas sequence plus one.

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