Question 20
Let $Q(z)$ and $R(z)$ be the unique polynomials such that $$
\begin{aligned} &z^{2021}+1 \\ &\quad = (z^2+z+1)Q(z)+R(z) \end{aligned}
$$ and the degree of $R$ is less than $2.$ What is $R(z)?$
\begin{aligned} &z^{2021}+1 \\ &\quad = (z^2+z+1)Q(z)+R(z) \end{aligned}
$$ and the degree of $R$ is less than $2.$ What is $R(z)?$