有关Euler函数φ（n）的方程的可解性问题

摘要

For any given positive integer n≥1,the famous Euler function φ( n) is defined to be the number of all positive integers not exceeding n which are relatively prime to n. The main purpose of this paper is to use the elementary method to study the solvability of the equation φ(xy) =5(φ(x)+φ( y) ) ,and gives all its solutions.%对任意正整数n≥1,著名的欧拉函数φ(n)定义为不大于n且与n互素的正整数的个数。利用初等方法研究了方程φ(xy)=5(φ(x)+φ(y))的可解性问题,并给出了所有正整数解。