%0 Journal Article
%T 关于方程Z(n<sup>2</sup>)=&phi;<sub>10</sub>(SL(n))的可解性研究<br>On the Solvability of Number-Theoretic Function Equation Z(n<sup>2</sup>)=&phi;<sub>10</sub>(SL(n))
%A 尹秘
%A 向万国
%A 王军
%J Advances in Applied Mathematics
%P 3096-3104
%@ 2324-8009
%D 2024
%I Hans Publishing
%R 10.12677/aam.2024.137295
%X 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<i>p</i>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。<br />
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 <i>p</i> 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.
%K 伪Smarandache函数，Smarandache LCM函数，广义欧拉函数，可解性<br>Pseudo-Smarandache Function
%K Smarandache LCM Function
%K Generalized Euler Function
%K Solvability
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=91210