Dynamical system proof of Fermat's little theorem: an alternative approach

Abstract

Fermat’s little theorem has been proved using different mathematical approaches, which majority of them are based on number theory. These approaches have only exposed the usability of Fermat’s little theorem for logical, linear and structural predictions. Only small numbers of attempts had only been made to proof Fermat’s little theorem from other perspectives. This paper exhibits an alternative approach to proof the Fermat’s little theorem via dynamical system. Two lemmas are proven with respect to a redefined function, Tn (x) in order to achieve the task.