International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/2205 2020 2020 Universidad Regional Autónoma de los Andes (UNIANDES), Ecuador Luis Albarracín Zambrano Universidad Regional Autónoma de los Andes (UNIANDES), Ecuador Fabricio Lozada Torres Universidad Regional Autónoma de los Andes (UNIANDES), Ecuador Bolívar Villalta Jadan College Of Pharmacy, AL-Farahidi University, Baghdad, Iraq Nabil Khuder Salman This paper is dedicated to studying the foundations of 7-plithogenic and 8-plithogenic number theory, where the central concepts about symbolic 7-plithogenic8-plithogenic integers will be discussed such as symbolic 7-plithogenic8-plithogenic Pythagoras triples and quadruples, symbolic 7-plithogenic8-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-plithogenic8-pithogenic number theory. 2023 2023 44 55 10.54216/IJNS.220404 https://www.americaspg.com/articleinfo/21/show/2205