方程φ_2(n)=2^(Ω(n))和φ_2(φ_2(n))=2^(Ω(n))的可解性

Solvability of Equations φ_2(n)= 2^(Ω(n)) and φ_2(φ_2(n))=2^(Ω(n))

利用初等数论的方法研究与广义欧拉函数有关的方程φ2(n)=2Ω(n)、φ2(φ2(n))=2Ω(n)的可解性,并获得方程的所有正整数解.

Euler function is one of the most important and meaningful kinds of function in elementary number theory,and generalized Euler function is a kind of function which is closely connected with Euler function.They have many similar properties, but also have some completely different properties. The equations φ（n）=2Ω（n）,φ（φ2（n））=2Ω（n） related with generalized Euler function is studied using elementary meth- od, and all positive integer solutions are obtained.