{"title":"Bartz-Marlewski equation with generalized Lucas components","authors":"H. Hashim","doi":"10.5817/am2022-3-189","DOIUrl":null,"url":null,"abstract":". Let { U n } = { U n ( P,Q ) } and { V n } = { V n ( P,Q ) } be the Lucas sequences of the first and second kind respectively at the parameters P ≥ 1 and Q ∈ {− 1 , 1 } . In this paper, we provide a technique for characterizing the solutions of the so-called Bartz-Marlewski equation x 2 − 3 xy + y 2 + x = 0 , where ( x,y ) = ( U i ,U j ) or ( V i ,V j ) with i , j ≥ 1. Then, the procedure of this technique is applied to completely resolve this equation with certain values of such parameters.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"7 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archivum Mathematicum","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5817/am2022-3-189","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
. Let { U n } = { U n ( P,Q ) } and { V n } = { V n ( P,Q ) } be the Lucas sequences of the first and second kind respectively at the parameters P ≥ 1 and Q ∈ {− 1 , 1 } . In this paper, we provide a technique for characterizing the solutions of the so-called Bartz-Marlewski equation x 2 − 3 xy + y 2 + x = 0 , where ( x,y ) = ( U i ,U j ) or ( V i ,V j ) with i , j ≥ 1. Then, the procedure of this technique is applied to completely resolve this equation with certain values of such parameters.
期刊介绍:
Archivum Mathematicum is a mathematical journal which publishes exclusively scientific mathematical papers. The journal, founded in 1965, is published by the Department of Mathematics and Statistics of the Faculty of Science of Masaryk University. A review of each published paper appears in Mathematical Reviews and also in Zentralblatt für Mathematik. The journal is indexed by Scopus.