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  • 标题:On the 2 k -step Jordan-Fibonacci sequence
  • 本地全文:下载
  • 作者:Omur Deveci ; Sait Taş ; A Kılıçman
  • 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
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