Generalized partial differential equation and Fermat's Last Theorem

The equivalence of Fermat's Last Theorem and the non-existence of solutions of a generalized nth order homogenous hyperbolic partial differential equa tion in three dimensions and periodic boundary conditions defined in a cubi c lattice is demonstrated for all positive integer, n > 2. For the case n = 2, choosing one variable as time, solutions are identified as either propa gating or standing waves. Solutions are found to exist in the corresponding problem in two dimensions.