Question 8
Let $P_{1}, P_{2}, \ldots, P_{2019}$ be nonconstant polynomials with real coefficients such that
$$
P_{1}\left(P_{2}(x)\right)=P_{2}\left(P_{3}(x)\right)=\ldots=P_{2019}\left(P_{1}(x)\right)
$$
for every real number $x$. Prove that $P_{1}=P_{2}=\ldots=P_{2019}$.
$$
P_{1}\left(P_{2}(x)\right)=P_{2}\left(P_{3}(x)\right)=\ldots=P_{2019}\left(P_{1}(x)\right)
$$
for every real number $x$. Prove that $P_{1}=P_{2}=\ldots=P_{2019}$.