The Non-existence of Perfect Cuboid

TL;DR

This paper proves that a perfect cuboid with all integer sides, face diagonals, and space diagonal does not exist, settling a long-standing open problem in number theory.

Contribution

It provides a rigorous proof demonstrating the non-existence of perfect cuboids, a problem that has remained unsolved for centuries.

Findings

No perfect cuboid exists with all integer sides and diagonals.

The proof rules out the possibility of such a cuboid.

This result confirms longstanding conjectures in number theory.

Abstract

A perfect cuboid, popularly known as a perfect Euler brick/a perfect box, is a cuboid having integer side lengths, integer face diagonals and an integer space diagonal. Euler provided an example where only the body diagonal became deficient for an integer value but it is known as an Euler brick. Nobody has discovered any perfect cuboid, however many of us have tried it. The results of this research paper prove that there exists no perfect cuboid.