与三个数论函数有关的两个方程的解

The Solutions of two Equations on Three Number-Theoretic Functions

讨论了与数论函数Euler函数φ（m），函数Ω（m）和函数ω（m）相关联的两个方程φ（m）=2Ω（m）＋ω（m）3Ω（m）＋ω（m）与φ（m）=2Ω（m）-ω（m）3Ω（m）-ω（m）的可解性，利用这三个数论函数的相关性质以及初等方法，给出这两个方程的解，其中函数Ω（m）为m的质因子个数函数，函数ω（m）为m的相异质因子个数函数．

The solvability of two equations φ（m）=2Ω（m）＋ω（m）3Ω（m）＋ω（m） and φ（m）=2Ω（m）-ω（m）3Ω（m）-ω（m） on Euler function φ（m）, function Ω（m） and function ω（m） were discussed. The integer solutions of their were given by using the property of the three number-theoretic functions and elementary methods, where function Ω（m） is the total number of prime factors of m, function ω（m）is the number of all different prime divisors of m.