关于方程Z(n²)=φ₁₀(SL(n))的可解性研究  

On the Solvability of Number-Theoretic Function Equation Z(n2)=φ10(SL(n))

作　　者：尹秘 向万国 王军 

机构地区：[1]云南民族大学数学与计算机科学学院,云南 昆明

出　　处：《应用数学进展》2024年第7期3096-3104,共9页Advances in Applied Mathematics

摘　　要：本文利用伪Smarandache函数、Smarandache LCM函数和广义Euler函数的基本性质,以及一些初等方法和技巧给出φ10(pα)的准确计算公式,其中p是素数,且α是正整数。由此,我们讨论数论函数方程Z(n2)=φ10(SL(n))的可解性,结论是:该方程无正整数解。This paper applies the basic properties of pseudo-Smarandache, Smarandache LCM and generalized functions, as well as some elementary methods and techniques to obtain an accurate calculation formulaφ10(pα), where p is a prime number andαis a positive integer. Based on this formula, We discuss number- theoretic functional equationsZ(n2)=φ10(SL(n)). It is concluded that there is no positive integer solution to this equation.

关 键 词：伪SMARANDACHE函数 Smarandache LCM函数 广义欧拉函数 可解性 

分 类 号：O15[理学—数学]