A strategy of numeric search for perfect cuboids in the case of the second cuboid conjecture

Abstract

A perfect cuboid is a rectangular parallelepiped whose edges, whose face diagonals, and whose space diagonal are of integer lengths. The problem of finding such cuboids or proving their non-existence is not solved thus far. The second cuboid conjecture specifies a subclass of perfect cuboids described by one Diophantine equation of tenth degree and claims their non-existence within this subclass. Regardless of proving or disproving this conjecture in the present paper the Diophantine equation associated with it is studied and is used in order to build an optimized strategy of computer-assisted search for perfect cuboids within the subclass covered by the second cuboid conjecture.