Year: 2012
Type: preprint
Abstract: A perfect cuboid is a rectangular parallelepiped with integer edges, integer face diagonals, and integer space diagonal. Such cuboids have not yet been found, but nor has their existence been disproved. Perfect cuboids are described by a certain system of Diophantine equations possessing an intrinsic $S_3$ symmetry. Recently these equations were factorized with respect to this $S_3$ symmetry and the factor equations were transformed into $E$-form. As appears, the transformed factor equations are explicitly solvable. Based on this solution, polynomial inverse problems are formulated in the present paper.
Source: arXiv (Cornell University)
Authors: Ramsden, John, Sharipov, Ruslan
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1526422300