江汉大学学报（自然科学版）2026，Vol.54Issue(3)：28-33,6.DOI:10.16389/j.cnki.cn42-1737/n.2026.03.003
数论函数方程φ2(n)=S(SL(n7,8))的可解性
The Solvability of the Number-Theoretic Function Equationφ2(n)=S(SL(n7,8))
摘要
Abstract
Elementary method was employed to investigate the solutions of the number-theoretic function equation φ2(n)=S(SL(nk))when k=7,8.The left-hand side of the equation contains the generalized Euler functionφ2(n),while the right-hand side of S(SL(nk))is the composition function of the Smarandache-LCM function and the Smarandache function.Based on the intrinsic properties of the generalized Euler function and the composite function,all positive integer solutions of the number-theoretic function equation were found.关键词
数论函数方程/广义欧拉函数/Smarandache函数/Smarandache LCM函数Key words
number-theoretic function equation/generalized Euler function/Smarandache function/Smarandache-LCM function分类
数理科学引用本文复制引用
蔡俊俊,黄静,刘雪铃..数论函数方程φ2(n)=S(SL(n7,8))的可解性[J].江汉大学学报（自然科学版）,2026,54(3):28-33,6.基金项目
安徽省教育厅自然科学研究重点项目(2024AH051311,2025AHGXZK31193) （2024AH051311,2025AHGXZK31193）
安徽省教学质量工程项目(2024dzxkc130) （2024dzxkc130）
