Imaginary Cities of the Diophantine equation $X^3+Y^3+Z^3=K$

TL;DR

This paper explores a novel graph representation of the Diophantine equation involving cubes, utilizing the concept of imaginary cities and De Bruijn cycles to analyze modular combinations.

Contribution

It introduces a new graph-based approach to study the Diophantine equation using imaginary cities and modular De Bruijn cycles.

Findings

Graph representation of the equation constructed

Identification of modular combinations on edges

Application of De Bruijn cycles to the graph

Abstract

The purpose of this article is to make a graph representation of the Diophantine equation $X^3+Y^3+X^3=K$ using the theory of "imaginary cities" for its construction and to determine the modular combinations on its edges with the De Bruijn cycles.