MathDB

Let

n

be a natural number, with the prime factorisation

n = p_1^{e_1} p_2^{e_2} \cdots p_r^{e_r}

where

p_1, \ldots, p_r

are distinct primes, and

e_i

is a natural number. Define

rad(n) = p_1p_2 \cdots p_r

to be the product of all distinct prime factors of

n

. Determine all polynomials

P(x)

with rational coefficients such that there exists infinitely many naturals

n

satisfying

P(n) = rad(n)

Problem Statement