On the x-coordinates of Pell equations that are sums of two Padovan numbers

Let [Formula: see text] be the sequence of Padovan numbers defined by [Formula: see text] , [Formula: see text] , and [Formula: see text] for all [Formula: see text] . In this paper, we find all positive square-free integers d such that the Pell equations [Formula: see text] with [Formula: see text]...

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Detalles Bibliográficos
Autor principal: Ddamulira, Mahadi
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2021
Materias:
Original Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7900383/
https://www.ncbi.nlm.nih.gov/pubmed/33678911
http://dx.doi.org/10.1007/s40590-021-00312-8
Descripción
Sumario:Let [Formula: see text] be the sequence of Padovan numbers defined by [Formula: see text] , [Formula: see text] , and [Formula: see text] for all [Formula: see text] . In this paper, we find all positive square-free integers d such that the Pell equations [Formula: see text] with [Formula: see text] , have at least two positive integer solutions (x, y) and [Formula: see text] such that both x and [Formula: see text] are sums of two Padovan numbers.

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