{"status": "success", "data": {"description_md": "Consider the polynomial\n\n$$P(x)=\\prod_{k=0}^{10}(x^{2^k}+2^k)=(x+1)(x^2+2)(x^4+4)\\cdots (x^{1024}+1024)$$<br>The coefficient of $x^{2012}$ is equal to $2^a$.  What is $a$?\n\n$\\textbf{(A)}\\ 5<br>\\qquad\\textbf{(B)}\\ 6<br>\\qquad\\textbf{(C)}\\ 7<br>\\qquad\\textbf{(D)}\\ 10<br>\\qquad\\textbf{(E)}\\ 24$\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>Consider the polynomial</p>&#10;<p> <span class=\"katex--display\">P(x)=\\prod_{k=0}^{10}(x^{2^k}+2^k)=(x+1)(x^2+2)(x^4+4)\\cdots (x^{1024}+1024)</span> <br/>The coefficient of  <span class=\"katex--inline\">x^{2012}</span>  is equal to  <span class=\"katex--inline\">2^a</span> .  What is  <span class=\"katex--inline\">a</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 5\\qquad\\textbf{(B)}\\ 6\\qquad\\textbf{(C)}\\ 7\\qquad\\textbf{(D)}\\ 10\\qquad\\textbf{(E)}\\ 24</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": "2012 AMC 12A Problem 20", "can_next": true, "can_prev": true, "nxt": "/problem/12_amc12A_p21", "prev": "/problem/12_amc12A_p19"}}