Equal and Odd of Generalized Euler Function for Successive Integers
Xia Linfeng
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
Euler function \(\varphi(n)\) and generalized Euler function \(\varphi_{e}(n)\) are two important functions in number theory. Using the idea of classified discussion and determination of prime types, we study the solutions of odd number of generalized Euler function equations \(\varphi_{e}(n)=\varphi_{e}(n+1)\) and obtain all the values satisfying the corresponding conditions, where \(e=2,3,4,6\).
Keywords: Euler function, generalized Euler function, odd