Research
On Fermat’s Last Theorem Matrix Version and Galaxies of Sequences of Circulant Matrices with Positive Integers as Entries
We construct sequences of triples of circulant matrices with positive integers as entries which are solutions of the equation We introduce Mouanda's choice function for matrices which allows us to construct galaxies of sequences of triples of circulant matrices with positive integers as entries. We give many examples of galaxies of circulant matrices. The characterization of the matrix solutions of the equation allows us to show that the equation 2) has no circulant matrix with positive integers as entries solutions. This allows us to prove that, in general, the equation 3) has no circulant matrix with positive integers as entries solutions. We prove Fermat's Last Theorem for eigenvalues of circulant matrices. Also, we prove Fermat's Last Theorem for complex polynomials over associated to circulant matrices.
Separability and a Lax Pair for the c_{2}{(1)} Toda lattice
We consider the Toda lattice associated to the twisted affine Lie algebra ð¶ð¶2 (1). It is well known that this system is a two-dimensional algebraic completely integrable system. By using algebraic geometric methods, we give a linearisation of the system by determining the linearizing variables. This allows us to explain a morphism between this system and the Mumford system. Finally, a Lax representation in terms of 2 x 2 matrices is constructed for this system.
