On Matrix Elliptic Curves and Matrix Solutions of the Exponential Diophantine Equation (X^{24}-I_{24})(Y^{24}-I_{24})=Z^{2}

Joachim Moussounda Mouanda; Djagwa Dehainsala; Kinvi Kangni

doi:10.33425/2690-8077.1110

Japan Journal of Research

On Matrix Elliptic Curves and Matrix Solutions of the Exponential Diophantine Equation (X^{24}-I_{24})(Y^{24}-I_{24})=Z^{2}

Joachim Moussounda Mouanda, Djagwa Dehainsala, Kinvi Kangni

10.33425/2690-8077.1110 Published: 10 Apr, 2024

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Abstract

We show that the structures of the matrix solutions of the matrix elliptic curves 2 3 6 EY X I : , α = +× ∈ α α  allow the construction of the matrix solutions of the equations 4 24 6 24 24 2 24 24 XY ZX IY I Z += − −= ,( )( ) . Mathematics Subject Classification(2010). 15B36, 11D61.