On Periodic Points of the Order of Appearance in the Fibonacci Sequence

dc.contributor.author	Trojovská, Eva
dc.date.accessioned	2025-12-05T09:04:53Z
dc.date.available	2025-12-05T09:04:53Z
dc.date.issued	2020
dc.description.abstract	Let (F-n)(n >= 0) be the Fibonacci sequence. The order of appearance z(n) of an integer n >= 1 is defined by z (n) = min{k >= 1 : n vertical bar F-k}. Marques, and Somer and Krizek proved that all fixed points of the function z (n) have the form n = 5(k) or 12 . 5(k). In this paper, we shall prove that z(n) does not have any k-periodic points, for k >= 2.	eng
dc.format	p. "Article Number: 773"
dc.identifier.doi	10.3390/math8050773
dc.identifier.issn	2227-7390
dc.identifier.obd	43876491
dc.identifier.uri	http://hdl.handle.net/20.500.12603/1026
dc.identifier.wos	000542738100109
dc.language.iso	eng
dc.peerreviewed	yes
dc.publicationstatus	postprint
dc.publisher	MDPI-Molecular diversity preservation international
dc.relation.ispartof	Mathematics, volume 8, issue: 5	eng
dc.relation.publisherversion	https://www.mdpi.com/2227-7390/8/5/773
dc.rights.access	Open Access
dc.rights.license	CC BY
dc.source.url	https://www.mdpi.com/2227-7390/8/5/773
dc.subject	diophantine equation	eng
dc.subject	Fibonacci number	eng
dc.subject	order of appearance	eng
dc.subject	p-adic valuation	eng
dc.subject	arithmetic dynamics	eng
dc.title	On Periodic Points of the Order of Appearance in the Fibonacci Sequence	eng
dc.type	article

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