{"status": "success", "data": {"description_md": "Let $b \\geq 2$ be an integer. Call a positive integer $n$ $b\\textit{-eautiful}$ if it has exactly two digits when expressed in base $b$, and these two digits sum to $\\sqrt{n}$. For example, $81$ is $13$-eautiful because $81=\\underline{6}$ $\\underline{3}_{13}$ and $6+3=\\sqrt{81}$. Find the least integer $b\\geq 2$ for which there are more than ten $b$-eautiful integers.\n\n\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": "

Let b \\geq 2 be an integer. Call a positive integer n b\\textit{-eautiful} if it has exactly two digits when expressed in base b, and these two digits sum to \\sqrt{n}. For example, 81 is 13-eautiful because 81=\\underline{6} \\underline{3}_{13} and 6+3=\\sqrt{81}. Find the least integer b\\geq 2 for which there are more than ten b-eautiful integers.

Leading zeroes must be inputted, so if your answer is 34, then input 034. Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 6, "problem_name": "2024 AIME II Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/24_aime_II_p15", "prev": "/problem/24_aime_II_p13"}}