【摘要】 对于Fibonacci数列{Fn}以及给定的正整数m,由Fn关于模m的最小非负剩余an,构成一个新的数列{an},称为Fibonacci数列的模数列.本文利用初等数论的知识和数学归纳法,证明了Fibonacci数列的模数列是周期数列,并且是纯周期数列.更多还原

【Abstract】 For the Fibonacci sequence {Fn} and positive integer m,the new sequence {an} which composed of least non-negative residue an of module m on Fn is called modular sequence of Fibonacci sequence.Based on the elementary number theory and mathematical induction,this paper proves that the modular sequence of Fibonacci sequence is both a periodic sequence and a simple periodic sequence.更多还原