We present an exact theory of the BEC-BCS crossover in the BEC regime, which treats explicitely dimers as made of two fermions. We apply our framework, at zero temperature, to the calculation of the equation of state. We find that, when expanding the chemical potential in powers of the density n up to the Lee-Huang-Yang order, proportional to n^3/2, the result is identical to the one of elementary bosons in terms of the dimer-dimer scattering length a_M, the composite nature of the dimers appearing only in the next order term proportional to n^2 .
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