Extension of Fermat’s last theorem in Minkowski natural spaces

Abstract

Minkowski natural (N + 1)-dimensional spaces constitute the framework where the extension of Fermat’s last theorem is discussed. Based on empirical experience obtained via computational results, some hints about the extension of Fermat’s theorem from (2 + 1)-dimensional Minkowski spaces to (N + 1)-dimensional ones. Previous experience permits to conjecture that the theorem can be extended in (3 + 1) spaces, new results allow to do the same in (4 + 1) spaces, with an anomaly present here but difficult to find in higher dimensions. In (N + 1) dimensions with N> 4 there appears an increased difficulty to find Fermat vectors, there is discussed a possible source of such an obstacle, separately of the combinatorial explosion associated to the generation of natural vectors of high dimension.