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We give a computer assisted proof of the full listing of centralconfiguration for $n$-body problem for Newtonian potential on the plane for$n=5,6,7$ with equal masses. We show all these central configurations have areflective symmetry with respect to some line. For $n=8,9,10$ we establish theexistence of central configurations without any reflectional symmetry.

Central configurations in planar $n$-body problem with equal masses for $n = 5, 6, 7$