On Symbolic 7-Plithogenic and 8-Plithogenic Number Theoretical Concepts

Luis Albarracín Zambrano¹, Fabricio Lozada Torres¹, Bolívar Villalta Jadan¹, Nabil Khuder Salman²

¹Universidad Regional Autónoma de los Andes (UNIANDES), Ecuador

²College Of Pharmacy, AL-Farahidi University, Baghdad, Iraq

Emails: uq.luisalbarracin@uniandes.edu.ec; ua.fabriciolozada@uniandes.edu.ec; us.bolivarvillalta@uniandes.edu.ec;  nsalman@uoalfarahidi.edu.iq

Abstract

This paper is dedicated to studying the foundations of 7-plithogenic and 8-plithogenic number theory, where the central concepts about symbolic 7-plithogenic/8-plithogenic integers will be discussed such as symbolic 7-plithogenic/8-plithogenic Pythagoras triples and quadruples, symbolic 7-plithogenic/8-plithogenic linear Diophantine equations, and the divisors. On the other hand, we prove that Euler's theorem is still true in the case of the symbolic 7-plithogenic/8-pithogenic number theory.

Keywords: symbolic 7-plithogenic integer; symbolic 7-plithogenic congruencies; symbolic 7-plithogenic phi-Euler's theorem; symbolic 8-plithogenic phi-Euler's theorem.