摘要
讨论了Euler函数方程φ(n)=2ω(n)3ω(n)5ω(n)的可解性,利用数论基本理论以及分类讨论的方法给出了当ω(n)=1,2,3时该方程的具体正整数解,并在当ω(n)≥4该方程有正整数解时,给出了ω(n)≥4时该方程正整数解的形式,从而解决该方程正整数解的问题。
The solvability of the arithmetic functional equationφ(n)=2ω(n)3ω(n)5ω(n)was studied.Using the basic theory of number theory and the method of classification,the specific positive integer solutions of it were obtained forω(n)=1,2,3;if the equation has positive integer solutions forω(n)≥4,the explicit form of positive integer solutions were obtained.Therefore,the problem of positive integer solutions of the equation was solved.
作者
张四保
ZHANG Sibao(School of Mathematics and Statistics,Kashi University,Kashi 844008,China)
出处
《南昌大学学报（理科版）》
CAS
北大核心
2019年第2期114-119,共6页
Journal of Nanchang University(Natural Science)
基金
新疆维吾尔自治区自然科学基金资助项目(2017D01A13)
关键词
EULER函数
可解性
正整数解
Euler function
solvability
positive integer solution
