Rational Points on Fermat’s Surfaces in Minkowski’s(N+1) - Dimensional Spaces and Extended Fermat’s Last Theorem: Mathematical Framework and Computational Results

Abstract

The Fermat last theorem, defined in (2+1)-dimensional Minkowski spaces, is discussed and extended in natural and rational Mikowski’s spaces. Several pieces of computational interest are given, with many practical examples. A definition of Fermat vector order, Fermat surfaces, and Fermat surface radius is given. Several conjectures are discussed, among them the existence of a Fermat theorem in (3+1)-dimensional Minkowski spaces.