We introduce Mouanda’s choice function for matrices which allows us to construct the galaxies of sequences of triples of circulant matrices with positive integers as entries. We give many examples of the galaxies of circulant matrices with positive integers as entries. The characterization of the matrix solutions of the equation allows us to show that the equation has no circulant matrix with positive integers as entries solutions. This allows us to prove that, in general, the equation has no circulant matrix with positive integers as entries solutions. We prove Fermat’s Last Theorem for eigenvalues of circulant matrices. Also, we show Fermat’s Last Theorem for complex polynomials over associated to circulant matrices.
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.