Asymptotic approach to the perfect cuboid problem

Abstract

The problem of perfect cuboids is one of the old unsolved problems in number theory. By means of various methods it can be reduced to finding a solution of some single Diophantine equation of high degree obeying certain restrictions in the form of inequalities. Each such Diophantine equation is called a characteristic equation of a perfect cuboid. In this paper we present the results obtained by applying asymptotic metods to one of the characteristic equations of a perfect cuboid in the case of the second cuboid conjecture. This results shrink the domain of the integer parameters of the considered characteristic equation and thus make more effective the computer search of perfect cuboids based on this equation.