Sequential and computational approach for obtaining the quadruples of a Diophantine System

Abstract

This manuscript is concerned with obtaining non-negative and non-zero sequential and computational solutions to the Diophantine problem, which states that the sum of four non-negative, non-zero integers, the sum of the squares of these integers, and their cubic sum are perfect squares. Hitherto, no sequential pattern has been discovered on this particular Diophantine form of four unknowns under specific conditions. An open question is further addressed at the end.