On Multiverses (or Parallel Universes) of Matrix Triple Solutions of the Diophantine Equation X3 + Y 6 = Z

Abstract

We show that the Diophantine equation X 3 + Y 6 = Z 6 (0.1) admits matrix triple solutions from M3(N) and M6k(N), k ∈ N. We construct infinite universes made of these solutions. We introduce different construction structures sets of matrix solutions associated to the Diophantine equation (0.1). These construction structures sets of matrix solutions allow us to show that there exists an infinite number of multiverses (parallel universes) of the matrix solutions of the Diophantine equation (0.1) containing each a finite number of universes of matrix triples.