| Since the generalized Euler function was proposed in 2007,it is an open problem to determine its explicit computing formula.Until now,the explicit computing formula of φ_e(n)is given only when e=3,4,6.Based on the explicit computing formula ofφ_e(n)(e=1,2),and the properties for S(n),SL(n)and φ_e(n),the solvability of the number theory equation S(SL(n~k))=φ_e(n)(k=1,2)is studied,and then all the positive integer solutions are determined.By using elementary methods and techniques,this thesis discusses the solvability of the number theory equation S(SL(n~k))=φ_e(n)(k=1,2),and the all positive integer solutions are determined when e=3,4,6. |
