Some problems related to the growth of z(n)

dc.rights.license	CC BY	eng
dc.contributor.author	Trojovský, Pavel	cze
dc.date.accessioned	2025-12-05T09:04:45Z
dc.date.available	2025-12-05T09:04:45Z
dc.date.issued	2020	eng
dc.identifier.issn	1687-1847	eng
dc.identifier.uri	http://hdl.handle.net/20.500.12603/1025
dc.description.abstract	Let (Fn)n >= 0 be the Fibonacci sequence. The order of appearance z(n) of a positive integer n is defined as z(n):=min{k >= 1:n divide Fk}. In 2013, Marques proved that lim infn ->infinity z(n)/n=0. Let epsilon be a positive real number. In this paper, in particular, we generalized this Marques' result by proving that almost all positive integers satisfy z(n)/n < epsilon.	eng
dc.format	p. "Article Number: 270"	eng
dc.language.iso	eng	eng
dc.publisher	Springer	eng
dc.relation.ispartof	Advances in difference equations, volume 2020, issue: 1	eng
dc.subject	Asymptotic	eng
dc.subject	Arithmetic functions	eng
dc.subject	Fibonacci sequence	eng
dc.subject	Order of appearance	eng
dc.subject	Natural density.	eng
dc.title	Some problems related to the growth of z(n)	eng
dc.type	article	eng
dc.identifier.obd	43876480	eng
dc.identifier.doi	10.1186/s13662-020-02735-5	eng
dc.publicationstatus	postprint	eng
dc.peerreviewed	yes	eng
dc.source.url	https://advancesindifferenceequations.springeropen.com/articles/10.1186/s13662-020-02735-5	cze
dc.relation.publisherversion	https://advancesindifferenceequations.springeropen.com/articles/10.1186/s13662-020-02735-5	eng
dc.rights.access	Open Access	eng