Two Equations Related to the Smarandache Function

For any natural number n, Smarandache function S(n) means the smallest positive integer m can satisfy n│m!. For any given positive integer n,the famous pseudo Smarandache function Z(n)is defined as the smallest positive integer m to make n│1+2+…m=m(m+1)2.. This paper uses elementary method to study the equation S(n)+Z(n)=n and S(n)=P(n), and gives their all solutions.