On Fermat's equation over 2-by-2 matrices integers modulo prime

Ibnu Hadi; Yudi Mahatma; Devi Eka Wardani Meganingtyas; Dini Zainati; Tiara Nabila

doi:10.1063/5.0244686

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On Fermat's equation over 2-by-2 matrices integers modulo prime

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Ibnu Hadi, Yudi Mahatma, Devi Eka Wardani Meganingtyas, Dini Zainati, Tiara Nabila

2024 AIP Conference Proceedings Vol. 3148 Issue 1 Conference paper Cited by 0 SDG 16

Abstract

In this paper we investigate the solvability of Fermat's matrix equation over the group of nonsingular matrices of integers modulo prime. Here we use literature review to construct the theories. It is obtained that the equation Xn + Yn = Z?n always has solution in GL2(Z2) and for n = 3 the equation has solution in GL2(Z3). This result can be extend more general to GLm(Zp), for m > 2 or p > 3. © 2024 Author(s).

Affiliations

Program Studi Matematika, Universitas Negeri Jakarta, Jalan Rawamangun Muka, Jakarta Timur, 13220, Indonesia

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