Open AccessThe Solutions of Generalized Euler Function Equation φ_2(n-φ_2 (n))=2ω(n)
Author(s) -
Yifan Xu,
Zhongyan Shen
Publication year - 2021
Publication title -
journal of advances in mathematics and computer science
Language(s) - English
Resource type - Journals
ISSN - 2456-9968
DOI - 10.9734/jamcs/2021/v36i430353
Subject(s) - integer (computer science) , euler's formula , mathematics , function (biology) , euler's totient function , euler equations , prime (order theory) , upper and lower bounds , pure mathematics , mathematical analysis , combinatorics , computer science , evolutionary biology , biology , programming language
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.