{"status": "success", "data": {"description_md": "Arithmetic sequences $\\left(a_n\\right)$ and $\\left(b_n\\right)$ have integer terms with $a_1=b_1=1<a_2 \\le b_2$ and $a_n b_n = 2010$ for some $n$. What is the largest possible value of $n$?\n\n$\\textbf{(A)}\\ 2 \\qquad \\textbf{(B)}\\ 3 \\qquad \\textbf{(C)}\\ 8 \\qquad \\textbf{(D)}\\ 288 \\qquad \\textbf{(E)}\\ 2009$\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>Arithmetic sequences  <span class=\"katex--inline\">\\left(a_n\\right)</span>  and  <span class=\"katex--inline\">\\left(b_n\\right)</span>  have integer terms with  <span class=\"katex--inline\">a_1=b_1=1&lt;a_2 \\le b_2</span>  and  <span class=\"katex--inline\">a_n b_n = 2010</span>  for some  <span class=\"katex--inline\">n</span> . What is the largest possible value of  <span class=\"katex--inline\">n</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 2 \\qquad \\textbf{(B)}\\ 3 \\qquad \\textbf{(C)}\\ 8 \\qquad \\textbf{(D)}\\ 288 \\qquad \\textbf{(E)}\\ 2009</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": "2010 AMC 12A Problem 20", "can_next": true, "can_prev": true, "nxt": "/problem/10_amc12A_p21", "prev": "/problem/10_amc12A_p19"}}