A Quadratic Diophantine Equation Involving Generalized Fibonacci Numbers

dc.contributor.author	Chaves, Ana Paula
dc.contributor.author	Trojovský, Pavel
dc.date.accessioned	2025-12-05T09:05:27Z
dc.date.available	2025-12-05T09:05:27Z
dc.date.issued	2020
dc.description.abstract	The sequence of the k-generalized Fibonacci numbers (F-n((k)))(n) is defined by the recurrence F-n((k)) = Sigma(k)(j) = 1 F-n-j((k)) beginning with the k terms 0,..., 0, 1. In this paper, we shall solve the Diophantine equation F-n((k)) = (F-m((l)))(2) + 1, in positive integers m, n, k and l.	eng
dc.format	p. "Article Number: 1010"
dc.identifier.doi	10.3390/math8061010
dc.identifier.issn	2227-7390
dc.identifier.obd	43876511
dc.identifier.scopus	2-s2.0-85087572684
dc.identifier.uri	http://hdl.handle.net/20.500.12603/1030
dc.identifier.wos	000550837900001
dc.language.iso	eng
dc.peerreviewed	yes
dc.publicationstatus	postprint
dc.publisher	MDPI-Molecular diversity preservation international
dc.relation.ispartof	Mathematics, volume 8, issue: 6	eng
dc.relation.publisherversion	https://www.mdpi.com/2227-7390/8/6/1010
dc.rights.access	Open Access
dc.rights.license	CC BY
dc.source.url	https://www.mdpi.com/2227-7390/8/6/1010
dc.subject	Fibonacci number	eng
dc.subject	recurrence sequence	eng
dc.subject	linear form in logarithms	eng
dc.subject	reduction method.	eng
dc.title	A Quadratic Diophantine Equation Involving Generalized Fibonacci Numbers	eng
dc.type	article

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