Open AccessEqual and Odd of Generalized Euler Function for Successive Integers
Author(s) -
Linfeng Xia,
Zhongyan Shen
Publication year - 2022
Publication title -
journal of advances in mathematics and computer science
Language(s) - English
Resource type - Journals
ISSN - 2456-9968
DOI - 10.9734/jamcs/2022/v37i230435
Subject(s) - euler's formula , mathematics , function (biology) , prime (order theory) , euler number (physics) , pure mathematics , euler's totient function , semi implicit euler method , euler equations , combinatorics , mathematical analysis , backward euler method , evolutionary biology , biology
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 \(e=2,3,4,6\).