{"status": "success", "data": {"description_md": "There exists a unique strictly increasing sequence of nonnegative integers $a_1 < a_2 <...<  a_k$ such that\n\n$$\\frac{2^{289}+1}{2^{17}+1} = 2^{a_1} + 2^{a_2} +...  + 2^{a_k}.$$What is $k?$\n\n$\\textbf{(A) } 117 \\qquad \\textbf{(B) } 136 \\qquad \\textbf{(C) } 137 \\qquad \\textbf{(D) } 273 \\qquad \\textbf{(E) } 306$\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>There exists a unique strictly increasing sequence of nonnegative integers <span class=\"katex--inline\">a_1 &lt; a_2 &lt;...&lt;  a_k</span> such that</p>&#10;<p><span class=\"katex--display\">\\frac{2^{289}+1}{2^{17}+1} = 2^{a_1} + 2^{a_2} +...  + 2^{a_k}.</span>What is <span class=\"katex--inline\">k?</span></p>&#10;<p><span class=\"katex--inline\">\\textbf{(A) } 117 \\qquad \\textbf{(B) } 136 \\qquad \\textbf{(C) } 137 \\qquad \\textbf{(D) } 273 \\qquad \\textbf{(E) } 306</span></p>&#10;<hr/>&#10;<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>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2020 AMC 12A Problem 19", "can_next": true, "can_prev": true, "nxt": "/problem/20_amc12A_p20", "prev": "/problem/20_amc12A_p18"}}