与Euler函数有关一个方程的正整数解

摘要

研究了不定方程φ(abcd)=2(φ(a)+φ(b)+φ(c)+φ(d))的可解性问题,利用初等方法给出了该方程所有的正整数解,其中φ(n)是Euler函数.%The main purpose of this paper is to study the solvability of the equation φp(abcd) =2(φ(a) + φ(b) + φ(c) + φ(d)),and all positive integer solutions were obtained by using the elementary method,where φ(n) is Euler function.