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Fermat's equation over 2-by-2 matrices
Mao-Ting Chien,Jie Meng 대한수학회 2021 대한수학회보 Vol.58 No.3
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.