Perfect cuboids and multisymmetric polynomials

Abstract

A perfect Euler cuboid is a rectangular parallelepiped with integer edges and integer face diagonals whose space diagonal is also integer. The problem of finding such parallelepipeds or proving their non-existence is an old unsolved mathematical problem. The Diophantine equations of a perfect Euler cuboid have an explicit $S_3$ symmetry. In this paper the cuboid equations are factorized with respect to their $S_3$ symmetry in terms of multisymmetric polynomials. Some factor equations are calculated explicitly.

AmSTeX, 12 pages, amsppt style

References in corpus (1)

• A note on the third cuboid conjecture. Part I

Cited by in corpus (10)

• On an ideal of multisymmetric polynomials associated with perfect cuboids
• A biquadratic Diophantine equation associated with perfect cuboids
• On the equivalence of cuboid equations and their factor equations
• Inverse problems associated with perfect cuboids
• On singularities of the inverse problems associated with perfect cuboids
• A note on rational and elliptic curves associated with the cuboid factor equations
• On two algebraic parametrizations for rational solutions of the cuboid equations
• On two elliptic curves associated with perfect cuboids
• A note on solutions of the cuboid factor equations
• On a pair of cubic equations associated with perfect cuboids