MathDB

Given a polynomial

P

and a positive integer

k

, we denote the

k

-fold composition of

P

P^{\circ k}

. A polynomial

P

with real coefficients is called perfect if for each integer

n

there is a positive integer

k

so that

P^{\circ k}(n)

is an integer. Is it true that for each perfect polynomial

P

, there exists a positive

m

so that for each integer

n

there is

0<k\leq m

for which

P^{\circ k}(n)

is an integer?

Problem Statement