Question 13
There is a polynomial $P(x)$ with integer coefficients such that $$
\begin{aligned} P(x) &= (x^{2310}-1)^6 \\ &\quad {}\cdot \frac{1}{(x^{105}-1)(x^{70}-1)} \\ &\quad {}\cdot \frac{1}{(x^{42}-1)(x^{30}-1)} \end{aligned}
$$ holds for every $0 \lt x \lt 1.$ Find the coefficient of $x^{2022}$ in $P(x).$
\begin{aligned} P(x) &= (x^{2310}-1)^6 \\ &\quad {}\cdot \frac{1}{(x^{105}-1)(x^{70}-1)} \\ &\quad {}\cdot \frac{1}{(x^{42}-1)(x^{30}-1)} \end{aligned}
$$ holds for every $0 \lt x \lt 1.$ Find the coefficient of $x^{2022}$ in $P(x).$