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Found problems: 1

2007 AIME Problems, 11
Tags: algebra , polynomial , axusus
For each positive integer $p$, let $b(p)$ denote the unique positive integer $k$ such that $|k-\sqrt{p}|<\frac{1}{2}$. For example, $b(6) = 2$ and $b(23)=5$. If $S = \textstyle\sum_{p=1}^{2007}b(p)$, find the remainder when S is divided by 1000.