{"status": "success", "data": {"description_md": "It is known that, for all positive integers $k,$<br>\n$$1^{2}+2^{2}+3^{2}+\\cdots+k^{2}=\\frac{k(k+1)(2k+1)}{6}. $$Find the smallest positive integer $k$ such that $1^{2}+2^{2}+3^{2}+\\cdots+k^{2}$ is a multiple of $200.$\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>It is known that, for all positive integers <span class=\"katex--inline\">k,</span><br/><span class=\"katex--display\">1^{2}+2^{2}+3^{2}+\\cdots+k^{2}=\\frac{k(k+1)(2k+1)}{6}. </span>Find the smallest positive integer <span class=\"katex--inline\">k</span> such that <span class=\"katex--inline\">1^{2}+2^{2}+3^{2}+\\cdots+k^{2}</span> is a multiple of <span class=\"katex--inline\">200.</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": "2002 AIME II Problem 7", "can_next": true, "can_prev": true, "nxt": "/problem/02_aime_II_p08", "prev": "/problem/02_aime_II_p06"}}