Three cuboid conjectures are three mathematical propositions claiming irreducibility of three univariate polynomials with integer coefficients depending on several integer parameters. They are neither proved nor disproved.
Contents
The first cuboid conjecture
Cuboid conjecture 1. For any two positive coprime integer numbers
is irreducible over the ring of integers
The second cuboid conjecture
Cuboid conjecture 2. For any two positive coprime integer numbers
is irreducible over the ring of integers
The third cuboid conjecture
Cuboid conjecture 3. For any three positive coprime integer numbers
is fulfilled the twelfth degree polynomial
is irreducible over the ring of integers
Background
The conjectures 1, 2, and 3 are related to the perfect cuboid problem. Though they are not equivalent to the perfect cuboid problem, if all of these three conjectures are valid, then no perfect cuboids exist.