Work

Resolution of Richard Guy's Problem D18: Complete Non-existence of Perfect Cuboids via Pell Equations, Linear Forms in Logarithms, and Human-AI Collaborative Methodology

Year: 2026

Type: article

Abstract: This paper investigates Richard Guy's Problem D18 concerning the existence of a perfect cuboid. By reducing the fundamental Pythagorean constraints into a coupled system of Pell's equations and applying Matveev's lower bound theorem for linear forms in logarithms, we derive an absolute upper bound for all hypothetical solutions and establish a rigorous non-existence proof across the infinite domain. Furthermore, this work reflects upon the methodological and epistemological significance of human-AI collaboration in advancing independent mathematical research.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.24051275

Author: 市田, 宗一郎

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7225575926

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