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

TL;DR

This paper applies Cayley-Dickson function theory, including residues and homotopy theorems, to explore Fermat's last theorem by constructing and analyzing a special meromorphic function over Cayley-Dickson algebras.

Contribution

It introduces a novel approach using Cayley-Dickson function theory and residues to study Fermat's last theorem, which is a new application of these mathematical tools.

Findings

Construction of a special meromorphic function over Cayley-Dickson variables

Application of homotopy and Rouché's theorems in Cayley-Dickson context

Insights into Fermat's last theorem via Cayley-Dickson function analysis

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.