{"status": "success", "data": {"description_md": "There exists a unique strictly increasing sequence of nonnegative integers $a_1 < a_2 < \\ldots < a_k$ such that$$\\frac{2^{289}+1}{2^{17}+1} = 2^{a_1} + 2^{a_2} + \\ldots + 2^{a_k}.$$What is $k?$\n\n$\\textbf{(A) } 117 \\qquad \\textbf{(B) } 136 \\qquad \\textbf{(C) } 137 \\qquad \\textbf{(D) } 273 \\qquad \\textbf{(E) } 306$", "description_html": "<p>There exists a unique strictly increasing sequence of nonnegative integers <span class=\"katex--inline\">a_1 &lt; a_2 &lt; \\ldots &lt; a_k</span> such that<span class=\"katex--display\">\\frac{2^{289}+1}{2^{17}+1} = 2^{a_1} + 2^{a_2} + \\ldots + 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;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2020 AMC 10A Problem 21", "can_next": true, "can_prev": true, "nxt": "/problem/20_amc10A_p22", "prev": "/problem/20_amc10A_p20"}}