MathDB

Let

n

be a positive integer, with prime factorization

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

for distinct primes

p_1, \ldots, p_r

and

e_i

positive integers. Define

rad(n) = p_1p_2\cdots p_r,

the product of all distinct prime factors of

n

.
Find all polynomials

P(x)

with rational coefficients such that there exists infinitely many positive integers

n

with

P(n) = rad(n)

Problem Statement