安徽大学学报（自然科学版）2025，Vol.49Issue(4)：1-7,7.DOI:10.3969/j.issn.1000-2162.2025.04.001
一类数论函数方程的可解性的讨论
Discussion on the solvability of a class of arithmetic function equations
摘要
Abstract
In order to simplify the discussion of positive integer solutions for equations of the formγ(ψ2(x))k=S(SL(xl)),the solvability of equation in the form of γ(ψ2(x))k=S(SL(xl))was discussed,some forms of its positive integer solutions for general equations and the scope for certain quantities when discussing positive integer solutions were provided.By using the given conclusions,two specific equations in the form of γ(ψ2(x))k=S(SL(xl))were discussed,and all their positive integer solutions were provided.关键词
广义Euler函数ψe(n)/Smarandache函数S(n)/Smarandache LCM(least common multiple)函数SL(n)/数论函数方程/正整数解Key words
generalized Euler function ψe(n)/Smarandache function S(n)/Smarandache LCM function SL(n)/arithmetic function equation/positive integer solution分类
数理科学引用本文复制引用
张四保,陈盈颖..一类数论函数方程的可解性的讨论[J].安徽大学学报（自然科学版）,2025,49(4):1-7,7.基金项目
新疆维吾尔自治区自然科学基金资助项目(2022D01A14) （2022D01A14）
新疆维吾尔自治区高校基本科研业务费科研项目(XJEDU2022P088) （XJEDU2022P088）
