{"status": "success", "data": {"description_md": "Let $Q(z)$ and $R(z)$ be the unique polynomials such that$$z^{2021}+1=(z^2+z+1)Q(z)+R(z)$$and the degree of $R$ is less than $2.$ What is $R(z)?$\n\n$\\textbf{(A) }{-}z \\qquad \\textbf{(B) }{-}1 \\qquad \\textbf{(C) }2021\\qquad \\textbf{(D) }z+1 \\qquad \\textbf{(E) }2z+1$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Let  <span class=\"katex--inline\">Q(z)</span>  and  <span class=\"katex--inline\">R(z)</span>  be the unique polynomials such that <span class=\"katex--display\">z^{2021}+1=(z^2+z+1)Q(z)+R(z)</span> and the degree of  <span class=\"katex--inline\">R</span>  is less than  <span class=\"katex--inline\">2.</span>  What is  <span class=\"katex--inline\">R(z)?</span> </p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) }{-}z \\qquad \\textbf{(B) }{-}1 \\qquad \\textbf{(C) }2021\\qquad \\textbf{(D) }z+1 \\qquad \\textbf{(E) }2z+1</span> </p>&#10;<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2021 AMC 12B Problem 20", "can_next": true, "can_prev": true, "nxt": "/problem/21_amc12B_p21", "prev": "/problem/21_amc12B_p19"}}