{"status": "success", "data": {"description_md": "Positive integers $a$, $b$, and $2009$, with $a<b<2009$, form a geometric sequence with an integer ratio. What is $a$? \n\n$\\mathrm{(A)}\\ 7\n\\qquad\n\\mathrm{(B)}\\ 41\n\\qquad\n\\mathrm{(C)}\\ 49\n\\qquad\n\\mathrm{(D)}\\ 289\n\\qquad\n\\mathrm{(E)}\\ 2009$", "description_html": "<p>Positive integers  <span class=\"katex--inline\">a</span> ,  <span class=\"katex--inline\">b</span> , and  <span class=\"katex--inline\">2009</span> , with  <span class=\"katex--inline\">a&lt;b&lt;2009</span> , form a geometric sequence with an integer ratio. What is  <span class=\"katex--inline\">a</span> ?</p>\n<p> <span class=\"katex--inline\">\\mathrm{(A)}\\ 7\n\\qquad\n\\mathrm{(B)}\\ 41\n\\qquad\n\\mathrm{(C)}\\ 49\n\\qquad\n\\mathrm{(D)}\\ 289\n\\qquad\n\\mathrm{(E)}\\ 2009</span> </p>\n<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": 1, "problem_name": "2009 AMC 10A Problem 9", "can_next": true, "can_prev": true, "nxt": "/problem/09_amc10A_p10", "prev": "/problem/09_amc10A_p08"}}