三变元非线性欧拉函数方程Φ(xyz)=Φ(x)(Φ(y)+Φ(z))的可解性  

The Solvability of Nonlinear Euler Function Equation Φ(xyz)=Φ(x)(Φ(y)+Φ(z))

作　　者：阳连武[1] 张华清 张军桃 YANG Lian-wu;ZHANG Hua-qing;ZHANG Jun-tao(College of Mathematics and Computer Science,Yichun University;The Experimental Middle School of Yichun City;The Third Primary School of Yichun City,Yichun 336000,China)

机构地区：[1]宜春学院数学与计算机科学学院 [2]宜春市实验中学 [3]宜春市第三小学,江西宜春336000

出　　处：《宜春学院学报》2023年第12期21-24,共4页Journal of Yichun University

摘　　要：利用初等数学方法和欧拉函数的若干性质,研究了三变元非线性欧拉函数方程Φ(xyz)=Φ(x)(Φ(y)+Φ(z))的可解性问题,证明了该方程的正整数解存在性定理,给出了该方程的正整数解的一般形式,并求出了当x≤20时该方程的所有正整数解。In this paper,the solvability of Nonlinear Euler function equation with three variables Φ(xyz)=Φ(x)(Φ(y)+Φ(z))is studied by using primary mathematical methods and some properties of Euler function.The existence theorem of positive integer solution of the equation is proved.A general form of positive integer solution of the equation is given,and all positive integer solutions of the equation are obtained when x≤20.

关 键 词：欧拉函数 非线性不定方程 正整数解 最大公因数 

分 类 号：O156[理学—数学]