If I have a set $A \subset \{1,2,3,...,\epsilon p \} \subset \mathbf{Z}/p \mathbf{Z}$ does there exist a dilation $ \lambda $ such that $ \lambda A$ has no gap larger than $s$ (where $\epsilon = s^{-1}$)? Obviously if A was the whole set then I could just take $s$ for the dilation factor, but what if A isn't the whole thing?
Dilation mod p, small gaps
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combinatorics
number-theory
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0What is $\epsilon p$? Might help to restate as e.g. $A$ subset of ${1,2,..,k}$ (for some fixed $k \le p$) and restate the gap question in terms of $k$. – 2012-11-04