{"status": "success", "data": {"description_md": "Let $a_0 = 2$, $a_1 = 5$, and $a_2 = 8$, and for $n>2$ define $a_n$ recursively to be the remainder when $4(a_{n-1} + a_{n-2} + a_{n-3})$ is divided by $11$. Find $a_{2018}\\cdot a_{2020}\\cdot a_{2022}$.\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 a_0 = 2, a_1 = 5, and a_2 = 8, and for n>2 define a_n recursively to be the remainder when 4(a_{n-1} + a_{n-2} + a_{n-3}) is divided by 11. Find a_{2018}\\cdot a_{2020}\\cdot a_{2022}.

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": 3, "problem_name": "2018 AIME II Problem 2", "can_next": true, "can_prev": true, "nxt": "/problem/18_aime_II_p03", "prev": "/problem/18_aime_II_p01"}}