Dynamical system proof of Fermat’s little theorem: An alternative approach


  • Olamide Funmilayo Florence Universiti Teknologi Malaysia
  • Tahir Ahmad Universiti Teknologi Malaysia
  • Adaraniwon Amos Olalekan University of Malaya




Fermat’s little theorem and dynamical system approach


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.

Author Biographies

Olamide Funmilayo Florence, Universiti Teknologi Malaysia

Department of Mathematical Sciences, Faculty of Science, 

Tahir Ahmad, Universiti Teknologi Malaysia

Centre for Sustainable Nanomaterials, Ibnu Sina Institute for Scientific and Industrial Research

Adaraniwon Amos Olalekan, University of Malaya

Institute of Mathematical Sciences, Faculty of Science


Iga, K. (2003). A dynamical systems proof of Fermat’s's little theorem. Mathematics magazine, 76(1), 48-51.

Holmgren, R. (2012). A first course in discrete dynamical systems. Springer Science & Business Media.