2012/07/17 by Ruslan Sharipov, Sharipov, Ruslan
Mathematics · #11D41 #11D72 #13A50 #13F20 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11D41 #msc:11D72 #msc:13A50 #msc:13F20
paper · pdf · doi:10.48550/arxiv.1207.4081
AmSTeX, 17 pages, amsppt style
arxiv created 2012/07/17 · arxiv updated 2012/07/18
A perfect Euler cuboid is a rectangular parallelepiped with integer edges and integer face diagonals whose space diagonal is also integer. Such cuboids are not yet discovered and their non-existence is also not proved. Perfect Euler cuboids are described by a system of four Diophantine equation possessing a natural S3 symmetry. Recently these equations were factorized with respect to this S3 symmetry and the factor equations were derived. In the present paper the factor equations are transformed to E-form and then reduced to a single biquadratic equation.