MathDB

Let

\sigma(S_n,k)

denote the sum of the

k

th powers of the lengths of the sides of the convex

n

-gon

S_n

inscribed in a unit circle. Show that for any natural number greater than

2

there exists a real number

k_0

between

1

and

2

such that

\sigma(S_n,k_0)

attains its maximum for the regular

n

-gon. L. Fejes Toth

Problem Statement