We investigate dense nuclear matter with a dibaryon Bose-Einstein condensate as a possible intermediate state before the quark-gluon phase transition. An exact analysis of this state of matter is presented in a one-dimensional model. The analysis is based on a reduction of the quantization rules for the N-body problem to N coupled algebraic transcendental equations. We observe that when the Fermi momentum approaches the resonance momentum, the one-particle distribution function increases near the Fermi surface. When the Fermi momentum is increased beyond the resonance momentum, the equation of state becomes softer. The observed behavior can be interpreted in terms of formation of a Bose-Einstein condensate of two-fermion resonances (dibaryons). In cold nuclear matter, it should occur if 2(m_N + epsilon_F) is greater or equal to m_D, where m_N and m_D are respectively the nucleon and dibaryon masses and epsilon_F is the nucleon Fermi energy.
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