Question 4
Let be given a positive integer $n \gt 1$. Find all polynomials $P(x)$ non constant, with real coefficients such that
$$
P(x) P\left(x^{2}\right) \ldots P\left(x^{n}\right) = P\left(x^{\frac{n(n+1)}{2}}\right)
$$
for all $x \in \mathbb{R}$.
$$
P(x) P\left(x^{2}\right) \ldots P\left(x^{n}\right) = P\left(x^{\frac{n(n+1)}{2}}\right)
$$
for all $x \in \mathbb{R}$.