| Fibonacci数列的性质及应用 |
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| 引用本文： | 张全超,刘丁酉.Fibonacci数列的性质及应用[J].湖北民族学院学报(哲学社会科学版),2009,27(1). |
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| 作者姓名： | 张全超 刘丁酉 |
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| 作者单位： | 张全超,ZHANG Quan-chao(武汉大学东湖分校,高等数学教研室,湖北,武汉,430212);刘丁酉,LIU Ding-you(武汉大学数学与统计学院,湖北,武汉,430072)
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| 基金项目： | 国家自然科学基金，云南省校合作项目 |
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| 摘 要： | 从数论的角度研究了Fibonacci数列{Fn}的性质,证明了任意两个Fibonacci数的最大公因数与它们序标的最大公因数之间的关系,得到了Fibonacci数为素数的必要条件;给出Fibonacci数列在正整数表示方面应用的算法和C程序,进一步加深了对Fibonacci数列的认识.
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| 关 键 词： | Fibonacci数列 素数 最大公约数 算法 程序 |
The Properties and Application of Fibonacci Sequence |
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| ZHANG Quan-chao,LIU Ding-you.The Properties and Application of Fibonacci Sequence[J].Journal of Hubei Institute for Nationalities(Natural Sciences),2009,27(1). |
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| Authors: | ZHANG Quan-chao LIU Ding-you |
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| Institution: | 1.Teaching and Research Division of Higher Mathematics;Donghu College;Wuhan University;Wuhan 430212;China;2.School of Mathematics and Statistics;Wuhan 430072;China |
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| Abstract: | In this paper,the properties of Fibonacci sequence {Fn} is investigated from the perspective of number theory,and the relation between the greatest common divisor(GCD) of Fm and Fn and the GCD of m and n is proved.Furthermore,the necessary condition for a Fibonacci number is a prime is obtained.In addition,the algorithm and C program are presented for an application of Fibonacci sequence in representation of the positive integer.The results enhance our knowledge of Fibonacci sequence. |
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| Keywords: | Fibonacci sequence prime greatest common divisor algorithm programm |
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