整数矩阵集上的Fermat方程

Fermat's equation in the set of integral matrices

设A 是 m 阶整数矩阵,A 是由A 的全体方幂构成的集合.本文证明了:当 m > 9 时,如果A 的行列式｜ A｜ ≠0 ,而且A 的特征根不全为单位根,则A 上的Fermat 方程无解.

Let A be an integral matrix of order m,and let A be the set of all powers of A.In this paper we prove that if m>9,the determinant ｜A｜=±1 and all eigenvalues of A are not total roots of unity,then Fermat's equation has no solution on A.