MathDB

You are given

N

such that

n \ge 3

. We call a set of

N

points on a plane acceptable if their abscissae are unique, and each of the points is coloured either red or blue. Let's say that a polynomial

P(x)

divides a set of acceptable points either if there are no red dots above the graph of

P(x)

, and below, there are no blue dots, or if there are no blue dots above the graph of

P(x)

and there are no red dots below. Keep in mind, dots of both colors can be present on the graph of

P(x)

itself. For what least value of k is an arbitrary set of

N

points divisible by a polynomial of degree

k

Problem Statement