Abstract
A uniform dilute Bose system with repulsive interactions is studied in the grand canonical ensemble formalism. We present a parametric equation of state that holds true from high temperatures down to below the transition temperature, thus providing a scheme for exploring the quantum-statistical nature of the Bose-Einstein condensation transition in interacting gases. As an application, the interaction-induced shift of the transition temperature is derived to be $\mathrm{\ensuremath{\Delta}}{T}_{c}∕{T}_{c}^{0}=2.83{n}^{1∕3}a$, where $n$ is the density and $a$ is the $S$-wave scattering length.
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