MathDB

Let

n\ge 3

be an integer. Let

f(x)

and

g(x)

be polynomials with real coefficients such that the points

(f(1),g(1)),(f(2),g(2)),\dots,(f(n),g(n))

\mathbb{R}^2

are the vertices of a regular

n

-gon in counterclockwise order. Prove that at least one of

f(x)

and

g(x)

has degree greater than or equal to n\minus{}1.

A5