This paper proves that there are at most four equilibrium points of the electric potential of three fixed point charges in R 2 when the three charges form an isosceles right triangle or an equilateral triangle.
In this article, we count the number of (N − 1)-dimensional central configurations of the restricted (N + 1)-body problem with equal masses. For N = 4, 5, there are 25, 56 central configurations. For N = 3 or N ≥ 6, the number of central configurations is 2 N + N − 1.
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