A Remark On Carmichael's Conjecture

In number theory,Euler's totient function counts the positive integers up to a given integer n that are relatively prime to n.Because this function was first studied by Euler in proving Fermat's little theorem,it is called Euler function,which is also called ?function or Euler total function The Carmichael's conjecture is a classical conjecture of number theory.Klee Masia and other mathematicians have done a variety of studies on this conjecture,but their work is limited to the study of computational number theory.Carl Pomerance was the first to study this conjecture theoretically,and proved a sufficient condition for this conjecture.In this paper,by studying the number of solutions n of the equation ?(n)= x,we provide new research ideas for Carmichael's conjecture.Finally,we find a necessary and sufficient condition of this conjecture,that is,Carmichael's conjecture is true if and only if it is true in the set {24337243k,k?N}.