MITPrimes Neural Codes - Question 6 (Polymath Problem)

Let $P$ be a polynomial with integer coefficients and at least $3$ simple roots. Is it true that $P(n)$ is a powerful integer only finitely often?

Note: A powerful integer is an integer $m$ such that if a prime $p \mid m$ , then $p^2 \mid m$ .

Source: 2018 MITPrimes - Neural Codes