| Fibonacci数列的模数列的周期性 |
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| 引用本文： | 袁明豪. Fibonacci数列的模数列的周期性[J]. 数学的实践与认识, 2007, 37(3): 119-122 |
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| 作者姓名： | 袁明豪 |
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| 作者单位： | 黄冈师范学院数学系,湖北,黄州,438000 |
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| 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.
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| 关 键 词： | Fibonacci数列 模数列 周期数列 纯周期数列 |
| 修稿时间： | 2005-09-19 |
The Periodicity of Modular Sequence of Fibonacci Sequence |
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| YUAN Ming-hao. The Periodicity of Modular Sequence of Fibonacci Sequence[J]. Mathematics in Practice and Theory, 2007, 37(3): 119-122 |
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| Authors: | YUAN Ming-hao |
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| 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. |
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| Keywords: | Fibonacci sequence modular sequence periodic sequence simple periodic sequence |
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