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There is no Perfect Cuboid

Ivor Lloyd

Abstract

A perfect cuboid is formed when an Euler brick whose edges and face diagonals are all integers also has an integer internal diagonal. It is known that if a perfect cuboid exists the internal diagonal is odd. No perfect cuboid has been found. This simple proof shows that the internal diaogonal of an Euler brick cannot be an odd integer.

There is no Perfect Cuboid

Abstract

A perfect cuboid is formed when an Euler brick whose edges and face diagonals are all integers also has an integer internal diagonal. It is known that if a perfect cuboid exists the internal diagonal is odd. No perfect cuboid has been found. This simple proof shows that the internal diaogonal of an Euler brick cannot be an odd integer.
Paper Structure (2 sections, 1 theorem, 10 equations)

This paper contains 2 sections, 1 theorem, 10 equations.

Table of Contents

  1. Introduction
  2. The proof

Key Result

Theorem 1

If all the edges and face diagonals in the Euler brick are positive integers then the internal diagonal is not integer.

Theorems & Definitions (1)

  • Theorem 1