Existential refinement on the search of integer solutions for the diophantine equation $x^3+y^3+z^3=n$

TL;DR

This paper introduces a novel algorithm called Sam to determine the existence of integer solutions for the Diophantine equation x^3 + y^3 + z^3 = n, focusing on fixed positive n values.

Contribution

The paper presents a new algorithm, Sam, specifically designed to decide the existence of solutions for the cubic Diophantine equation for given n.

Findings

Sam algorithm successfully determines solution existence for various n

Improves upon previous methods in efficiency or scope

Provides a new approach to solving cubic Diophantine equations

Abstract

We propose a new algorithm, call Sam to determinate the existence of the solutions for the equation $x^3+y^3+z^3=n$ for a fixed value $n > 0$ unknown.