有关Euler函数φ(n)的方程的可解性问题

The Solvability Problems of an Equation on Euler Function φ( n)

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。

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（γ） ）,and gives all its solutions.