Quick note #1: Its obvious if A is an 1 by 1 matrix or A is diagonalizable.Let A be a non singular integer square matrix with integer entries. Suppose that for every positive integer k, there is a matrix X with integer entries such that $X^{k}=A$. Prove that A must be the identity matrix
Quick note #2: Cavachi - the owner of this problem - is pretty famous himself for proposals of difficult arithmetic problems in MAA Monthly. So if you can solve it, you can have the feeling of beating a big dude
Bài viết đã được chỉnh sửa nội dung bởi Bio Rua: 01-05-2009 - 13:56