  The well-known results concerning a dilute Bose gas with the short-range
repulsive interaction should be reconsidered due to a thermodynamic
inconsistency of the method being basic to much of the present understanding of
this subject and nonrelevant behaviour of the pair distribution function at
small boson separations. The aim of our paper is to propose a new way of
treating the dilute Bose gas with an arbitrary strong interaction. Using the
reduced density matrix of the second order and a variational procedure, this
way allows us to escape the inconsistency mentioned and operate with singular
potentials like the Lennard-Jones one. All the consideration concerns the zero
temperature.
