摘要
设n,e>1均为正整数,利用初等的方法和技巧,以及伪Smarandache函数Z(n).Smarandache LCM函数SL(n)和广义Euler函数φ_(e)(n)的基本性质,讨论数论函数方程Z(SL(n))=φ_(e)(n)(e=3,4,6)的可解性,并给出其全部的正整数解.
Let n,e>1 be positive integers. By using elementary methods and techniques, in addition to the properties for the pseudo-Smarandache function, the Smarandache LCM function and the generalized Euler function, this paper discusses the positive integer solutions for the equation Z(SL(n))=φ_(e)(n) when e∈{3,4,6}, and determines its all positive integer solutions.
作者
杜珊
廖群英
王慧莉
DU Shan;LIAO Qunying;WANG Huili(School of Mathematical Sciences,Sichuan Normal University,Chengdu 610066,Sichuan)
出处
《四川师范大学学报(自然科学版)》
CAS
2022年第1期21-26,共6页
Journal of Sichuan Normal University(Natural Science)
基金
国家自然科学基金(12071321)。