The Solutions For Two Classes Of Number Theory Equations

Depending on the exact formula of the generalized Euler function φe(n)(e=3,4),and elementary methods,the solvability of the equation φe(φe(n))=3Ω(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 α be a positive integer.Denote ρ(pα)=pα-pα-1+pα-2-…＋(-1)α.Suppose that n is a positive integer with two distinct prime divisors,all positive integer solutions of the equation kρ(n)=n+d(k=3,4)are obtained,where 1 ≤d<n and d | n.