Fermat's equation over 2-by-2 matrices
Bull. Korean Math. Soc. 2021 Vol. 58, No. 3, 609-616
https://doi.org/10.4134/BKMS.b200403
Published online February 22, 2021
Printed May 31, 2021
Mao-Ting Chien, Jie Meng
Soochow University; 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 : Primary 15A24, 11D41
Supported by : Jie Meng was partially supported by National Research Foundation of Korea (NRF) Grant funded by the Korean Government (MSIP) (NRF-2017R1A5A1015722)
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