The Solutions of Generalized Euler Function Equation φ_2(n-φ_2 (n))=2ω(n)

Abstract

By using the properties of Euler function, an upper bound of solutions of Euler function equation is given, where is a positive integer. By using the classification discussion and the upper bound we obtained, all positive integer solutions of the generalized Euler function equation are given, where is the number of distinct prime factors of n.