On Fermat’s Last Theorem and Galaxies of Sequences of Positive Integers

Abstract

We construct sequences of positive integers which are solutions of the equation x 2 +y 2 =z 2 . We introduce Mouanda’s choice functions which allow us to construct galaxies of sequences of positive integers. We give many examples of galaxies of numbers. We show that the equation x 2n +y 2n =z 2n (n ≥ 2) has no integer solutions. We prove that the equation x n +y n =z n (n ≥ 3 ) has no solutions in N . We introduce the notion of the planetary representation of a galaxy of numbers which allow us to predict the structure, laws of the universe and life in every planet system of every galaxy of the universe. We show that every multiverse contains a finite number of universes.