| 广义Fibonacci函数的整数值 |
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| 引用本文： | 田永祺.广义Fibonacci函数的整数值[J].西北大学学报,2012(2):173-176. |
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| 作者姓名： | 田永祺 |
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| 作者单位： | 内蒙古财经学院统计与数学学院 |
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| 基金项目： | 国家自然科学基金资助项目(11071194) |
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| 摘 要： | 目的讨论广义Fibonacci函数F(a,x)的性质,并求出所有有理数r使得F(a,r)为正整数。方法利用初等方法以及Pell方程的性质。结果给出了所有可使F(a,x)是正整数的有理数r。结论获得了所有可使F(a,x)为正整数的有理数r的具体表示形式。
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| 关 键 词： | 广义Fibonacci函数 整数值 Pell方程 |
The integral values of generalized Fibonacci functions |
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| TIAN Yong-qi.The integral values of generalized Fibonacci functions[J].Journal of Northwest University(Natural Science Edition),2012(2):173-176. |
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| Authors: | TIAN Yong-qi |
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| Institution: | TIAN Yong-qi(School of Mathematics and Statistics,Inner Mongolia Finance and Economics College,Hohhot 010051,China) |
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| Abstract: | Aim Discussing the properties of the generalized Fibonacci function,and finding all rational number r such that F(a,r) is a positive integer.Methods Using the elementary method and the properties of the Pell′s equation.Results All rational numbers r for which F(a,r) are positive integers have been given.Conclusion An exact expression of the rational number r is obtained for which F(a,r) is a positive integer. |
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| Keywords: | generalized Fibonacci function integral value Pell′s equation |
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