{"status": "success", "data": {"description_md": "The [[polynomial]] $x^3 - 2004 x^2 + mx + n$ has [[integer]] coefficients and three distinct positive zeros. Exactly one of these is an integer, and it is the sum of the other two.  How many values of $n$ are possible?\n\n$\\mathrm{(A)}\\ 250,000<br>\\qquad\\mathrm{(B)}\\ 250,250<br>\\qquad\\mathrm{(C)}\\ 250,500<br>\\qquad\\mathrm{(D)}\\ 250,750<br>\\qquad\\mathrm{(E)}\\ 251,000$\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>The [[polynomial]]  <span class=\"katex--inline\">x^3 - 2004 x^2 + mx + n</span>  has [[integer]] coefficients and three distinct positive zeros. Exactly one of these is an integer, and it is the sum of the other two.  How many values of  <span class=\"katex--inline\">n</span>  are possible?</p>&#10;<p> <span class=\"katex--inline\">\\mathrm{(A)}\\ 250,000\\qquad\\mathrm{(B)}\\ 250,250\\qquad\\mathrm{(C)}\\ 250,500\\qquad\\mathrm{(D)}\\ 250,750\\qquad\\mathrm{(E)}\\ 251,000</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": 5, "problem_name": "2004 AMC 12B Problem 23", "can_next": true, "can_prev": true, "nxt": "/problem/04_amc12B_p24", "prev": "/problem/04_amc12B_p22"}}