20. Let $Q(z), R(z)$ satisfy
$$
z^{2021}+1=\left(z^{2}+z+1\right) Q(z)+R(z)
$$

the unique polynomials, where $\operatorname{deg} R(z)<2$. Then $R(z)=$ ( ).
(A) $-z$
(B) -1
(C) 2021
(D) $z+1$
(E) $2 z+1$
20. A.
$$
\begin{aligned}
\text { Given } & z^{3}-1 \equiv 0\left(\bmod z^{2}+z+1\right) \\
\Rightarrow & z^{2021}+1 \\
= & \left(z^{3}-1\right)\left(z^{2018}+z^{2015}+\cdots+z^{2}\right)+ \\
& \quad\left(z^{2}+z+1\right)-z \\
\equiv & -z\left(\bmod z^{2}+z+1\right) .
\end{aligned}
$$

Therefore, $R(z)=-z$.