2012/08/06 by Руслан Шарипов, Ruslan Sharipov, Sharipov, Ruslan · 1 citation
Computer Science · Mathematics · #11D25 #11D72 #12E05 #14E05 #14G05 #14H52 #Algebraic Geometry and Number Theory #FOS: Mathematics #Mathematics and Applications #Number Theory (math.NT) #Polynomial and algebraic computation #math.NT #msc:11D25 #msc:11D72 #msc:12E05 #msc:14E05 #msc:14G05 #msc:14H52
paper · pdf · doi:10.48550/arxiv.1208.1227
AmSTeX, 11 pages, amsppt style
arxiv created 2012/08/06 · openalex publication_date 2012/08/06 · arxiv updated 2012/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A rational perfect cuboid is a rectangular parallelepiped whose edges and face diagonals are given by rational numbers and whose space diagonal is equal to unity. Finding such a cuboid is equivalent to finding a perfect cuboid with all integer edges and diagonals, which is an old unsolved problem. Recently, based on a symmetry approach, it was shown that edges and face diagonals of rational perfect cuboid are roots of two cubic equations whose coefficients depend on two rational parameters. Six special cases where these cubic equations are reducible have been already found. Two more possible cases of reducibility for these cubic equations are considered in the present paper. They lead to a pair of elliptic curves.