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2013 AIME II Problems/Problem 14

Revision as of 16:33, 4 April 2013 by Yrushi (talk | contribs) (Problem 14)
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For positive integers $n$ and $k$, let $f(n, k)$ be the remainder when $n$ is divided by $k$, and for $n > 1$ let $F(n) = \max_{\substack{1\le k\le \frac{n}{2}}} f(n, k)$. Find the remainder when $\sum\limits_{n=20}^{100} F(n)$ is divided by $1000$.

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