Learning Concerning The Pseudo Smarandache Function And Its Related Functions

In this dissertation，the properties of some Smarandache functions are discussed byusing the elementary and analytic methods，and asymptotic formulas，positive integersolutions of special equations and residue theory related with these functions aregiven． Specifically the main achievements contained in this dissertation are as follows：Some asymptotic formulas involving are studied by using the elementary and analyticmethods， which are based on the properties of the pseudo Smarandache squarefreefunctionZ_w(n)，near pseudo Smarandache function K(n)and three arithmeticalfunctions and．By using the elementary method， the conditions that the pseudo Smarandachefunction Z(n)is a residue of d thdegree modulo n is discussed and the concreteforms of these conditions are given．Two equations concerning the pseudo Smarandache squarefree function Z w n，thepseudo Smarandache function Z(n)and the Smarandache ceil function S k n arediscussed and the concrete forms of their positive integer solutions are given．...