On the Pythagorean Triples’ Equations and the Perfect Cuboid Problem.

EasyChair Preprint 5241

Abstract

The perfect cuboid problem is a Pythagorean problem in nature. This paper gives several propositions regarding Pythagorean relationships and a discussion is made on the perfect cuboid problem. Among the proposi- tions is that the cuboid problem is a divisibility by 3 problem. Violation of the divisibility means that a perfect cuboid doesn’t exist for a given integer. Another consequence of divisibility by 3 and other theorems is that the fastest and most accurate algorithm for generating a random prime number p is, p = ((5 × β)^2 + 1)/2 where β = 2k + 1, k ∈ N.

Keyphrases: Euler Brick, Perfect Cuboid, Pythagorean, perfect cuboid problem, primitive Pythagorean triple

@booklet{EasyChair:5241,
  author    = {Alex Nguhi and Cleophas Kweyu},
  title     = {On the Pythagorean Triples’ Equations and the Perfect Cuboid Problem.},
  howpublished = {EasyChair Preprint 5241},
  year      = {EasyChair, 2021}}