{"status": "success", "data": {"description_md": "Let $f(x) = (x^2+3x+2)^{\\cos(\\pi x)}$. Find the sum of all positive integers $n$ for which $$\\left| \\sum_{k=1}^n \\log_{10} f(k) \\right| = 1. $$\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full 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>Let <span class=\"katex--inline\">f(x) = (x^2+3x+2)^{\\cos(\\pi x)}</span>. Find the sum of all positive integers <span class=\"katex--inline\">n</span> for which <span class=\"katex--display\">\\left| \\sum_{k=1}^n \\log_{10} f(k) \\right| = 1.</span></p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. 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": 4, "problem_name": "2014 AIME II Problem 7", "can_next": true, "can_prev": true, "nxt": "/problem/14_aime_II_p08", "prev": "/problem/14_aime_II_p06"}}