广义Lucas分量的Bartz-Marlewski方程

IF 0.5 Q3 MATHEMATICS

Archivum Mathematicum Pub Date : 2022-01-01 DOI:10.5817/am2022-3-189

H. Hashim

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引用次数: 0

摘要

。令{U n} = {U n (P,Q)}和{V n} = {V n (P,Q)}分别为参数P≥1和Q∈{−1,1}时的第一类和第二类卢卡斯序列。本文给出了一种描述所谓Bartz-Marlewski方程x 2−3 xy + y 2 + x = 0，其中(x,y) = (U i,U j)或(V i,V j)且i, j≥1的解法。然后，将该方法应用于具有一定参数值的方程的完全解。

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Bartz-Marlewski equation with generalized Lucas components

. 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.

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来源期刊

Archivum Mathematicum MATHEMATICS-

CiteScore

0.70

自引率

16.70%

发文量

审稿时长

35 weeks

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.