方程Z(SL(n))=φe(n)(e=3,4,6)的正整数解

The Positive Integral Solutions for the Equation Z(SL(n))=φ;(n)(e=3,4,6)

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.