The Solutions of Generalized Euler Function Equation φ_2(n-φ_2 (n))=2ω(n)
Xu Yifan
Department of Mathematics, Zhejiang International Studies University, Hangzhou 310023, P.R. China.
Shen Zhongyan *
Department of Mathematics, Zhejiang International Studies University, Hangzhou 310023, P.R. China.
*Author to whom correspondence should be addressed.
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.
Keywords: Euler functions, generalized Euler functions, solutions