Download PDFOpen PDF in browserOn the Pythagorean Triples’ Equations and the Perfect Cuboid Problem.EasyChair Preprint 524116 pages•Date: March 30, 2021AbstractThe 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
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