On the Nonexistence of Centered Co-Circular Central Configurations With Three Unequal masses

This paper examines the existence of centered co-circular central configurations in the general power-law potential n-body problem. We prove the nonexistence of such configurations when the system consists of n-3 equal masses and three arbitrary masses, under the condition that the three special masses are distinct or, if two of them are equal, not arranged in a specific manner.