The Solvability For Several Classes Of Number Theory Equations

For positive integers n and e(e?n),since the generalized Euler function?e(n)of a positive integer n was proposed in 2007,the explicit computing formula for ?e(n)is obtained only for the case e=1,2,3,4,6.And then,most of equations related to the generalized Euler function,Pseudo-Smarandache function or Smarandache LCM function are discussed only for the case e=1,2.Therefore,based on the properties for those functions,by using elementary methods and techniques,this thesis discusses the solvability for the number theory equation SL(n)=?e(n)(e?{2,3,4,6} or e|?(n)),Z(SL(n))=?e(n)(e=3,4,6)or Z(n2)=?e(SL(n)(e?{1,2,3,4,6}),respectively.Furthemore,the all positive integer solutions are obtained when they are solvable.