Abstract
This research investigates centered co-circular central configurations in the general power-law potential n-body problem. Firstly, there are no centered co-circular central configurations exist when precisely n−2 of the masses are equal; secondly, unless all masses are equal, no such configurations exist when masses can be divided into two sets of equal masses; thirdly, no such configurations exist when masses is a mix of equal masses and some heavier (lighter) ones, arranged such that the heavier (lighter) ones are non-adjacent.
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