{"status": "success", "data": {"description_md": "For positive integers $n$ and $k$, let $f(n,k)$ be the remainder when $n$ is divided by $k$, and for $n>1$ let $F(n) = \\displaystyle\\max_{1 \\le k \\le \\frac{n}{2}} f(n,k)$. Find the remainder when $\\displaystyle\\sum_{n=20}^{100} F(n)$ is divided by $1000$.\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": "

For positive integers n and k, let f(n,k) be the remainder when n is divided by k, and for n>1 let F(n) = \\displaystyle\\max_{1 \\le k \\le \\frac{n}{2}} f(n,k). Find the remainder when \\displaystyle\\sum_{n=20}^{100} F(n) is divided by 1000.

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": "2013 AIME II Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/13_aime_II_p15", "prev": "/problem/13_aime_II_p13"}}