文章基本信息

标题：On the 2 k -step Jordan-Fibonacci sequence
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作者：Omur Deveci ; Sait Taş ; A Kılıçman 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2017
卷号：2017
期号：1
页码：121
DOI：10.1186/s13662-017-1178-2
语种：English
出版社：Hindawi Publishing Corporation
摘要：In this paper, we define the 2k-step Jordan-Fibonacci sequence, and then we study the 2k-step Jordan-Fibonacci sequence modulo m. Also, we obtain the cyclic groups from the multiplicative orders of the generating matrix of the 2k-step Jordan-Fibonacci sequence when read modulo m, and we give the relationships among the orders of the cyclic groups obtained and the periods of the 2k-step Jordan-Fibonacci sequence modulo m. Furthermore, we extend the 2k-step Jordan-Fibonacci sequence to groups, and then we examine this sequence in the finite groups. Finally, we obtain the period of the 2k-step Jordan-Fibonacci sequence in the generalized quaternion group Q 2 n $Q_{2^{n}}$ as applications of the results produced.
关键词：Jordan-Fibonacci sequence ; group ; matrix ; period