| In 2007,Cai,etc,defined the generalized Euler function φe(n)of positive integer n(e∈ Z+).and gave an accurate calculation formula for φe(n)(e = 3,4,6).This thesis further studies the accurate calculation formula of the generalized Euler function.Based on the definitions of the generalized Euler function and Mobius function,the calculation formula ofφ5(n)for several classes of positive integers is obtained,and then the parity of φ5(n)is studied.Finally,by using elementary methods and techniques,the equation φe(n)= n/d(e = 1,2,3,4)is studied,the positive integer solutions for the above equation are given when e = 1,2,4 and the necessary condition for the existence of the solutions is also obtained for the case e = 3. |
