MathDB

Let

P(x)

be a nonzero polynomial of degree

n>1

with nonnegative coefficients such that function

y=P(x)

is odd. Is that possible thet for some pairwise distinct points

A_{1}, A_{2}, \dots A_{n}

on the graph

G: y = P(x)

the following conditions hold: tangent to

G

A_{1}

passes through

A_{2}

, tangent to

G

A_{2}

passes through

A_{3}

\dots

, tangent to

G

A_{n}

passes through

A_{1}

Problem Statement