| 关于含伪Smarandache函数及其对偶函数的方程的可解性 |
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| 引用本文： | 吴欣. 关于含伪Smarandache函数及其对偶函数的方程的可解性[J]. 西南大学学报(自然科学版), 2011, 33(8) |
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| 作者姓名： | 吴欣 |
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| 作者单位： | 西北大学数学系; |
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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： | 研究方程Z(n)+Z*(n)=n的可解性.利用初等方法和组合方法,借助同余方程,通过分类讨论证明了该方程有无限多个正整数解,并给出所有解的具体形式,彻底解决了2个猜想.
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| 关 键 词： | 伪Smarandache函数 对偶函数 可解性 方程 |
The Solvability for an Equation Involving the Pseudo-Smarandache Function and Its Dual Function |
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| WU Xin. The Solvability for an Equation Involving the Pseudo-Smarandache Function and Its Dual Function[J]. Journal of southwest university (Natural science edition), 2011, 33(8) |
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| Authors: | WU Xin |
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| Affiliation: | WU Xin Department of Mathematics,Northwest University,Xi'an 710127,China |
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| Abstract: | The solvability of the equation Z(n)+Z*(n)=n is studied.It is proved that the equation has infinite positive integer solutions,and all concrete forms of every solution are confirmed by using the elementary combinatorial method,especially via congruent equation.Finally,two conjectures are solved. |
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| Keywords: | pseudo-Smarandache function dual function solvability equation |
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