<?xml version="1.0" encoding="UTF-8"?><OAI-PMH xmlns="http://www.openarchives.org/OAI/2.0/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/ http://www.openarchives.org/OAI/2.0/OAI-PMH.xsd"><responseDate>2026-10-19T00:02:27Z</responseDate><request verb="GetRecord" identifier="oai:ebyu-rdlopen.rawdatalibrary.net:ebyu/14844" metadataPrefix="oai_dc">https://ebyu-rdlopen.rawdatalibrary.net/oai/request</request><GetRecord><record><header><identifier>oai:ebyu-rdlopen.rawdatalibrary.net:ebyu/14844</identifier><datestamp>2026-10-18T20:29:38Z</datestamp><setSpec>openaire</setSpec><setSpec>driver</setSpec><setSpec>com_ebyu_10000</setSpec><setSpec>col_ebyu_10001</setSpec></header><metadata><oai_dc:dc xmlns:oai_dc="http://www.openarchives.org/OAI/2.0/oai_dc/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd"><dc:title>On relationship among a new family of k-fibonacci, k-lucas numbers, fibonacci and lucas numbers</dc:title><dc:creator>Özkan, Engin</dc:creator><dc:creator>Altun, İpek</dc:creator><dc:creator>Göçer, Ali Aykut</dc:creator><dc:subject>Fibonacci numbers</dc:subject><dc:subject>Generalized fibonacci numbers</dc:subject><dc:subject>Lucas numbers</dc:subject><dc:subject>Period</dc:subject><dc:subject>Recurrance relation</dc:subject><dc:description>We prove some theorems concerning a family of Fibonacci numbers defined in [11]. We give some relationship between the family of Fibonacci and Lucas numbers. Then we define a new family of k-Lucas numbers and prove some properties of it related to the Lucas numbers and the family of Lucas numbers. © 2017, Chiang Mai University. All rights reserved.</dc:description><dc:publisher>Chiang Mai University</dc:publisher><dc:date>2017</dc:date><dc:type>Article</dc:type><dc:identifier>https://rdlopen.rawdatalibrary.net/r/ebyu/14844</dc:identifier><dc:identifier>0125-2526</dc:identifier><dc:language>en</dc:language><dc:relation>Chiang Mai Journal of Science</dc:relation><dc:rights>info:eu-repo/semantics/openAccess</dc:rights><dc:type>info:eu-repo/semantics/article</dc:type><dc:identifier>https://ebyu-rdlopen.rawdatalibrary.net/tr/items/ebyu/14844</dc:identifier></oai_dc:dc></metadata></record></GetRecord></OAI-PMH>