Consider the polynomial $p(x)=x^{2021}-x+1$, calculate the sum $$
r_{1}^{2021}+r_{2}^{2021}+\ldots+r_{n}^{2021}
$$
where $r_i$ are the 2021 roots of $p$
I'm not sure how to start, I know that can be done with Moivre's formula but I don't get any result.

If $a$ is a root of $x^n-x+1=0, a^n=a-1=y$(say)
$$\implies(y+1)^n-y=0\implies y^n+ny^{n-1}+\cdots+1=0$$
$$\implies\sum_{k=1}^nr_k=-\dfrac n1$$
