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Differences in a subset give all possible differences

Source: QEDMO 2005

November 8, 2005
floor function

Problem Statement

Prove: From the set {1,2,...,n}\{1,2,...,n\}, one can choose a subset with at most 2⌊n⌋+12 \left\lfloor \sqrt n \right\rfloor +1 elements such that the set of the pairwise differences from this subset is {1,2,...,n−1}\{1,2,...,n-1\}. (⌊x⌋\left\lfloor x \right\rfloor means the greatest integer ≤x\leq x)
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