MathDB

Let a polynomial

f(x)

be given with real coefficients and has degree greater or equal than 1. Show that for every real number

c > 0

, there exists a positive integer

n_0

satisfying the following condition: if polynomial

P(x)

of degree greater or equal than

n_0

with real coefficients and has leading coefficient equal to 1 then the number of integers

x

for which

|f(P(x))| \leq c

is not greater than degree of

P(x)

Problem Statement