  In a mixture of two kinds of identical bosons there are two types of pairs,
identical bosons' pairs, of either species, and pairs of distinguishable
bosons. In the present work fragmentation of pairs in a trapped mixture of
Bose-Einstein condensate is investigated using a solvable model, the symmetric
harmonic-interaction model for mixtures. The natural geminals for pairs made of
identical or distinguishable bosons are explicitly contracted by diagonalizing
the intra-species and inter-species reduced two-particle density matrices,
respectively. Properties of pairs' fragmentation in the mixture are discussed,
the role of the mixture's center-of-mass and relative center-of-mass
coordinates is elucidated, and a generalization to higher-order reduced density
matrices is made. As a complementary result, the exact Schmidt decomposition of
the wavefunction of the bosonic mixture is constructed. The entanglement
between the two species is governed by the coupling of their individual
center-of-mass coordinates, and it does not vanish at the limit of an infinite
number of particles where any finite-order intra-species and inter-species
reduced density matrix per particle is 100\% condensed. Implications are
briefly discussed.
