THE k-GENERALIZED LUCAS NUMBERS CLOSE TO A POWER OF 2

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dc.contributor.authorAcikel, Abdullah
dc.contributor.authorIrmak, Nurettin
dc.contributor.authorSzalay, Laszlo
dc.date.accessioned2024-09-18T20:28:16Z
dc.date.available2024-09-18T20:28:16Z
dc.date.issued2023
dc.departmentHatay Mustafa Kemal Üniversitesien_US
dc.description.abstractLet k >= 2 be a fixed integer. The k-generalized Lucas sequence {L-n((k))}(n)>=(0) starts with the positive integer initial values k, 1, 3, ..., 2(k-1)-1, and each term afterward is the sum of the k consecutive preceding elements. An integer n is said to be close to a positive integer m if n satisfies |n-m| < root m. In this paper, we combine these two concepts. We solve completely the diophantine inequality |L-n((k)) - 2(m) | < 2(m/2) in the non-negative integers k, n, and m. This problem is equivalent to the resolution of the equation L-n((k)) = 2(m) + t with the condition |t| < 2(m/2), t is an element of Z. We also discovered a new formula for L-n((k)) which was very useful in the investigation of one particular case of the problem.en_US
dc.description.sponsorshipNational Research, Development and Innovation Office [2019-2.1.11-TET-2020-00165]; Hungarian National Foundation for Scientific Research [128088, 130909]; Slovak Scientific Grant Agency [VEGA 1/0776/21]en_US
dc.description.sponsorshipFor L. Szalay, the research was supported in part by National Research, Development and Innovation Office Grant 2019-2.1.11-TET-2020-00165, by Hungarian National Foundation for Scientific Research Grant No. 128088 and No. 130909, and by the Slovak Scientific Grant Agency VEGA 1/0776/21.en_US
dc.identifier.doi10.1515/ms-2023-0064
dc.identifier.endpage882en_US
dc.identifier.issn0139-9918
dc.identifier.issn1337-2211
dc.identifier.issue4en_US
dc.identifier.scopus2-s2.0-85168093054en_US
dc.identifier.scopusqualityQ2en_US
dc.identifier.startpage871en_US
dc.identifier.urihttps://doi.org/10.1515/ms-2023-0064
dc.identifier.urihttps://hdl.handle.net/20.500.12483/10818
dc.identifier.volume73en_US
dc.identifier.wosWOS:001043701900005en_US
dc.identifier.wosqualityQ2en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherWalter De Gruyter Gmbhen_US
dc.relation.ispartofMathematica Slovacaen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectk-generalized Lucas sequenceen_US
dc.subjectBaker methoden_US
dc.subjectLLL reductionen_US
dc.titleTHE k-GENERALIZED LUCAS NUMBERS CLOSE TO A POWER OF 2en_US
dc.typeArticleen_US

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