MathDB

There are non-constant polynom

P(x)

with integral coefficients and natural number

n

. Suppose that

a_0=n

a_k=P(a_{k-1})

for any natural

k

. Finally, for every natural

b

there is number in sequence

a_0, a_1, a_2, \ldots

that is

b

-th power of some natural number that is more than 1. Prove that

P(x)

is linear polynom.

Problem Statement