Let σ(Sn,k) denote the sum of the kth powers of the lengths of the sides of the convex n-gon Sn inscribed in a unit circle. Show that for any natural number greater than 2 there exists a real number k0 between 1 and 2 such that σ(Sn,k0) attains its maximum for the regular n-gon.
L. Fejes Toth advanced fieldsadvanced fields unsolved