A note on the first cuboid conjecture

Abstract

Recently the problem of constructing a perfect Euler cuboid was related with three conjectures asserting the irreducibility of some certain three polynomials depending on integer parameters. In this paper a partial result toward proving the first cuboid conjecture is obtained. The polynomial which, according to this conjecture, should be irreducible over integers is proved to have no integer roots.

AmSTeX, 6 pages, amsppt style

References in corpus (3)

• Curves on the surface of cuboids
• Perfect cuboids and irreducible polynomials
• A note on a perfect Euler cuboid

Cited by in corpus (18)

• A note on the second cuboid conjecture. Part I
• A note on the third cuboid conjecture. Part I
• On an ideal of multisymmetric polynomials associated with perfect cuboids
• Perfect cuboids and multisymmetric polynomials
• On the equivalence of cuboid equations and their factor equations
• A biquadratic Diophantine equation associated with perfect cuboids
• Inverse problems associated with perfect cuboids
• On singularities of the inverse problems associated with perfect cuboids
• On two algebraic parametrizations for rational solutions of the cuboid equations
• A note on rational and elliptic curves associated with the cuboid factor equations
• On two elliptic curves associated with perfect cuboids
• A note on solutions of the cuboid factor equations
• A strategy of numeric search for perfect cuboids in the case of the second cuboid conjecture
• Asymptotic estimates for roots of the cuboid characteristic equation in the linear region
• Reverse asymptotic estimates for roots of the cuboid characteristic equation in the case of the second cuboid conjecture
• A note on invertible quadratic transformations of the real plane
• On a pair of cubic equations associated with perfect cuboids
• A fast modulo primes algorithm for searching perfect cuboids and its implementation