摘要
对任意的正整数n,函数φ(n)为著名的Euler函数,即在序列1,2,...,n-1,n中与n互质的整数的个数;函数ω(n)表示任意正整数n的所有不同质因数的个数。文章利用初等方法研究了φ(φ(n))=2ω(n)方程的可解性,并给出了该方程的全部正整数解。
The function Ч（n） is the famous Euler＇s totient function for arbitrary positive integer n, i.e. theintegral individual number of coprime with n in the sequencel,2 n-l,n. The function to （n） expresses individual number of all different prime-factor numbers of arbitrary integer n. In the present paper, the solvability of equation Ч（Ч（n））=2ω（n） was studied and all the positive integer solutions of the equation were given by using the elementary methods.
关键词
EULER函数
约数函数
正整数解
Euler＇s totient function
Divisor function
Positive integer solution
