Lucas数列的模数列的周期性  

The Periodicity of Modular Sequence of Lucas Sequence

作　　者：陈小芳[1] 

机构地区：[1]渭南师范学院数学与信息科学学院,陕西渭南714000

出　　处：《首都师范大学学报（自然科学版）》2015年第5期11-12,31,共3页Journal of Capital Normal University：Natural Science Edition

摘　　要：针对Lucas数列{Ln}以及给定的正整数m,由Ln关于模m的最小非负剩余bn构成一个新的数列{bn},称为Lucas数列的模数列.利用初等数论的相关知识和数学归纳法,证明了Lucas数列的模数列是周期数列,并且是纯周期数列.For the Lucas sequence { Ln} and positive integer m,the new sequence {bn} which composed of least non-negative residue bnof module m on Lnis called module sequence of Lucas sequence.Based on the elementary number theory and mathematical induction,this paper proves that the modular sequence of Lucas sequence is both a periodic sequence and a simple periodic sequence.

关 键 词：LUCAS数列 模数列 周期数列 纯周期数列 

分 类 号：O156.2[理学—数学]