ABSTRACT
In this paper, we study a particular class of matrices generated by generalized permutation matrices corresponding to a subgroup of some permutation group. As applications, we first present a technique from which we can get closed formulas for the roots of many families of polynomial equations with degree between 5 and 10, inclusive. Then, we describe a tool that shows how to find solutions to Fermat's last theorem and Beal's conjecture over the square integer matrices of any dimension. Finally, simple generalizations of some of the concepts in number theory to integer square matrices are presented.
Acknowledgements
The authors sincerely thank the reviewer and the editor for their valuable comments and helpful suggestions on an early version of this manuscript, which led to a substantial improvement on the presentation and contents of this paper.
Disclosure statement
No potential conflict of interest was reported by the authors.