Diophantine方程x^n+y^n=z^(φ(n))的本原解

The Primitive Solutions of the Diophantine Equation x^n+y^n=z^(φ(n))

设n是正整数,φ(n)是Euler函数.证明了方程xn+yn=zφ(n)当且仅当n≤3时有正整数解(x,y,z)适合gcd(x,y)=1.

Let n be a positive integer, and let φ（n） denote Euler＇s function. In this paper we prove that the equation x^n＋y^n=z^（φ（n）） has positive integer solutions（x,y,z） with gcd（x,y）=1 if and only if it is n≤3.