A note on the third cuboid conjecture. Part I
arXiv:1203.2567
Abstract
The problem of finding perfect Euler cuboids or proving their non-existence is an old unsolved problem in mathematics. The third cuboid conjecture is the last of the three propositions suggested as intermediate stages in proving the non-existence of perfect Euler cuboids. It is associated with a certain Diophantine equation of the order 12. In this paper a structural theorem for the solutions of this Diophantine equation is proved.
AmSTeX, 34 pages, amsppt style
Cited by in corpus (11)
- Perfect cuboids and multisymmetric polynomials
- 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