{"status": "success", "data": {"description_md": "Let $S$ be the set of positive integers $k$ such that the two parabolas $$y=x^2-k~~\\text{and}~~x=2(y-20)^2-k $$intersect in four distinct points, and these four points lie on a circle with radius at most $21$. Find the sum of the least element of $S$ and the greatest element of $S$.\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\">S</span> be the set of positive integers <span class=\"katex--inline\">k</span> such that the two parabolas<span class=\"katex--display\">y=x^2-k~~\\text{and}~~x=2(y-20)^2-k</span>intersect in four distinct points, and these four points lie on a circle with radius at most <span class=\"katex--inline\">21</span>. Find the sum of the least element of <span class=\"katex--inline\">S</span> and the greatest element of <span class=\"katex--inline\">S</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": 6, "problem_name": "2021 AIME I Problem 15", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/21_aime_I_p14"}}