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| 摘要: |
| 伪Smarandache函数、Smarandache LCM函数以及广义Euler函数都是重要的数论函数,本文研究了由这三类函数组成的数论函数方程Z(n2)=αe(SL(n2))的可解性问题.利用整除的性质和同余的方法, 获得了该方程在e=6时无正整数解的结果.推广了数论函数方程i>Z(n2)=α6(SL(n2))无正整数解的结果. |
| 关键词: 伪Smarandache函数 Smarandache LCM函数 广义Euler函数 |
| DOI： |
| 分类号:O156.1 |
| 基金项目:国家自然科学基金项目(11471007);陕西省科技厅科学技术研究发展计划项目(2013JQ1019);延安大学研究生教改研究项目(YDYJG2018022). |
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| SOLVABILITY OF A CLASS OF EQUATIONS CONTAINING GENERALIZED EULER FUNCTIONS |
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NIU Jia-xing,GAO Li
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| Abstract: |
| Pseudo Smarandache functions, Smarandache LCM and Euler functions are important number theoretic functions. In this paper, the solvability of the number theoretic functional equation Z(n2)=αe(SL(n2)) composed of these three classes of functions is studied. By using the property of integral division and the method of congruence, the result that equation has no positive integer solution at e=6 is obtained. This paper generalizes the result of the equation Z(n2)=α6(SL(n2)) without positive integer solution. |
| Key words: pseudo Smarandache function Smarandache LCM function generalized Euler function |
