Residues of functions of Cayley-Dickson variables and Fermat's last theorem

Abstract

Function theory of Cayley-Dickson variables is applied to Fermat's last theorem. For this the homotopy theorem, Rouch\'e's theorem and residues of meromorphic functions over Cayley-Dickson algebras are used. A special meromorphic function of Cayley-Dickson variables is constructed and its properties are investigated.