关于欧拉函数方程ϕ（ϕ（x））=2t的可解性

摘要

The function ϕ(n) is the famous Euler’s totient function for arbitrary positive integer n, i.e. it is the integral individual number of coprime with in the sequence 1, 2, · · · , n−1, n. In the present paper, the solvability of equationϕ(ϕ(x))=2t was studied and all the positive integer solutions of the equation were given by using the elementary methods.%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 中与n 互质的整数的个数。本文利用初等方法研究了方程ϕ(ϕ(x))的可解性,并给出了该方程的全部正整数解。