摘要
Fibonacci数列的模数列是周期数列,并且是纯周期数列.利用模数列的定义,讨论了Fibonacci数列的模数列的周期的一个性质,证明了下列结果:假设m1与m2为不同的正整数,Fibonacci数列{Fn}的模数列{an(m1)}与{an(m2)}的最小正周期分别为T1与T2,则模数列{an([m1,m2])}的最小正周期为[T1,T2].
The modular sequence of Fibonacci sequence is the periodic sequence as well as a simple periodic sequence. Based on the definition of modular sequence, this paper discusses a character of the period of modular sequence of Fibonacci Sequence. Then the following conclusion is obtained . If m1 and m2 are different positive integers, and the least positive periods of the modular sequence （αn（m1）} and （αn（m2）} of Fibonacci sequence {Fn} are T1 and T2 respectively, then the least positive period of the modular sequence （αn（[m1 ,m2]）} is [T1,T2].
出处
《数学的实践与认识》
CSCD
北大核心
2008年第8期207-210,共4页
Mathematics in Practice and Theory
