| Fibonacci数列的模数列的周期的一个性质 |
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| 引用本文： | 袁明豪. Fibonacci数列的模数列的周期的一个性质[J]. 数学的实践与认识, 2008, 38(8): 207-210 |
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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： | 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].
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| 关 键 词： | Fibonacci数列 模数列 最小正周期 最小公倍数 |
| 修稿时间： | 2007-03-21 |
A Character of the Period of Modular Sequence of Fibonacci Sequence |
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| YUAN Ming-hao. A Character of the Period of Modular Sequence of Fibonacci Sequence[J]. Mathematics in Practice and Theory, 2008, 38(8): 207-210 |
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| Authors: | YUAN Ming-hao |
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| Abstract: | 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 {an(m1)} and {an(m2)} of Fibonacci sequence {Fn} are T1 and T2 respectively,then the least positive period of the modular sequence {an([m1,m2])} is [T1,T2]. |
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| Keywords: | Fibonacci sequence modular sequence least positive period least common multiple |
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