2012/07/29 by John Ramsden, Ramsden, John, Руслан Шарипов +2
Computer Science · Engineering · Mathematics · #11D41 #11D72 #13A50 #13F20 #Coding theory and cryptography #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT) #graph theory and CDMA systems #math.NT #msc:11D41 #msc:11D72 #msc:13A50 #msc:13F20
paper · pdf · doi:10.48550/arxiv.1207.6764
AmSTeX, 11 pages, amsppt style
arxiv created 2012/07/29 · openalex publication_date 2012/07/29 · arxiv updated 2012/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 S3 symmetry. Recently these equations were factorized with respect to this S3 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.