Fermat's equation over 2-by-2 matrices
Bull. Korean Math. Soc.
Published online February 22, 2021
Mao-Ting Chien and Jie Meng
Soochow University, Taiwan, Pusan National University
Abstract : We study the solvability of the Fermat's matrix equation in some classes of 2-by-2 matrices. We prove the Fermat's matrix equation has infinitely many solutions in a set of 2-by-2 positive semidefinite integral matrices, and has no nontrivial solutions in some classes including 2-by-2 symmetric rational matrices and stochastic quadratic field matrices.
Keywords : Fermat's matrix equation; commuting family of matrices; stochastic matrices.
MSC numbers : 15A24, 11D41
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