Equal and Odd of Generalized Euler Function for Successive Integers
Journal of Advances in Mathematics and Computer Science · pp. 41–49 · Published 4 Apr 2022
10.9734/jamcs/2022/v37i230435Abstract
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 \(e=2,3,4,6\).
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