MathDB

5. On a circle consider

n

points among which there acts a repulsive force inversely proportional to the square of their distance. Prove that the point system is in stable equilibrium if and only if the points form a regular

n

-gon; in other words, considering the sum of the reciprocal distances of the

\binom{n}{2}

pairs of points which can be chosen from among the

n

given points, this sum is minimal if and only if the points lie at the vertices of a regular

n

-gon. (G. 2)

Problem Statement