A note on the first cuboid conjecture

2011/09/12 by Sharipov, Ruslan · 1 citation
#11D41 #11D72 #12E05 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1109.2534

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.

Cited by

• Irreducibility of the Cuboid Polynomial P_a,u(t) via a Rank-Zero Elliptic Curve

Related

• A note on the second cuboid conjecture. Part I
• A note on the third cuboid conjecture. Part I
• A note on a perfect Euler cuboid
• On an ideal of multisymmetric polynomials associated with perfect cuboids
• On the Irreducibility of the Cuboid Polynomial P_a,u(t)