Perfect cuboid, primitive Pythagorean triples and Eulerian parallelepipeds. Dynamics of construction

TL;DR

This paper proves that a perfect cuboid, a rectangular box with all edges and diagonals as integers, does not exist, resolving a long-standing open problem in number theory.

Contribution

The paper provides a proof demonstrating the non-existence of perfect cuboids, settling a major open question in the study of Pythagorean triples and Eulerian parallelepipeds.

Findings

Proof of non-existence of perfect cuboids

Clarification of constraints on integer edges and diagonals

Advancement in understanding Pythagorean structures

Abstract

One unsolved mathematical problem remains the perfect cuboid problem. A perfect cuboid is a rectangular parallelepiped whose edges, face diagonals and space diagonal are all expressed as integers. No such cuboid has yet been discovered and its existence has also not been proven. This paper shows a proof of the non-existence of a perfect cuboid.