含有伪Smarandache函数的方程的求解问题

摘要

利用初等方法及解析方法研究了两类包含伪Smarandache函数Z(n)的方程的可解性,证明了伪Smarandache函数Z(n)为n的原根当且仅当n=2,3,4.方程∑nk=1Z(k)=n(n+1)2有且仅有两个正整数解.%In this paper,the elementary and analytic methods are used to study the solvability of two classes of equations involving pseudo Smarandache functionZ(n).It is proved that if and only if n=2,3,4,the pseudo Smarandache function Z(n) is primitive root of n,Moreover,only two positive integer solutions of equation ∑nk-1Z(k)=n(n+1)2 is obtained.