Fermat Dynamics, Matrix Arithmetics, Finite Circles, and Finite Lobachevsky Planes
Arnold, Vladimir (2004), Fermat Dynamics, Matrix Arithmetics, Finite Circles, and Finite Lobachevsky Planes, Functional Analysis and its Applications, 38, 1, p. 1-13. http://dx.doi.org/10.1023/B:FAIA.0000024863.06462.68
TypeArticle accepté pour publication ou publié
Journal nameFunctional Analysis and its Applications
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Abstract (EN)Congruences generalizing Fermat's little theorem are proved for the traces of powers of integer matrices. Their relations to Lobachevsky geometries over finite fields and combinatorics of the matrix squaring operation as well as to the corresponding Riemann surfaces with their Kepler cubes are discussed.
Subjects / Keywordsarithmetics; symmetric function; trace; de Sitter world; Fermat's little theorem; Lobachevsky geometry; Kepler cube; Riemann surface
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