关于广义Fibonacci矩阵集合上的Fermat方程

On Fermat's Equation in the Set of Generalized Fibonacci Matrices

设Am是阶广义Fibonacci矩阵,设B={Akm|k∈Z,k≥0}.证明了:方程xn+yn=zn,x,y,z∈B,n∈N,n≥2没有解(n,x,y,z).

Let Am be the generalized Fibonacci matrix of order m and let B={Am^k ｜k∈Z,k≥0}. In this. paper we prove that the equation x^n＋y^n=z^n,x,y,z∈B,n∈N,n≥2 has no solution （ n, x, y, z）.