  In the present paper we study the low density Bose gas in the thermodynamic
limit interacting via two-body and three-body interaction potentials. We prove
that the leading order of the ground state energy is entirely characterised by
both the scattering length of the two-body potential and the scattering energy
of the three-body potential. The corresponding result for two-body interactions
was proven in seminal papers of Dyson (1957) and of Lieb-Yngvason (1998), and
the result for three-body interactions was proven by Nam-Ricaud-Triay. The
present result resolves a conjecture of Nam-Ricaud-Triay.
