The Solutions For Two Classes Of Number Theory Equations

Depending on the exact formula of the generalized Euler function ?e(n)(e=3,4),and elementary methods,the solvability of the equation ?e(?e(n))=3?(n)(e=3,4)is studied.Some sufficient conditions for the nonsolvability and two sufficient conditions for the solvability are obtained,and then all the corresponding positive solutions are determined.On the other hand7 let p be a prime,and ? be a positive integer.Denote ?(p?)=p?-p?-1+p?-2-…?(-1)?.Suppose that n is a positive integer with two distinct prime divisors,all positive integer solutions of the equation k?(n)=n+d(k=3,4)are obtained,where 1 ?d<n and d | n.