MathDB

The polynomials

f(x)

and

g(x)

are given. The points

A_1(f(1),g(1)),\ldots,A_n(f(n),g(n))

are marked on the coordinate plane. It turns out that

A_1\ldots A_n

is a regular

n{}

-gon. Prove that the degree of at least one of

f{}

and

g{}

is at least

n-1

.
Proposed by V. Bragin

Problem Statement