MathDB

For a nonnegative integer

n

define

\operatorname{rad}(n)=1

n=0

n=1

, and

\operatorname{rad}(n)=p_1p_2\cdots p_k

where

p_1<p_2<\cdots <p_k

are all prime factors of

n

. Find all polynomials

f(x)

with nonnegative integer coefficients such that

\operatorname{rad}(f(n))

divides

\operatorname{rad}(f(n^{\operatorname{rad}(n)}))

for every nonnegative integer

n

N5