IMO Shortlist 2003 problem C1


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April 2, 2012
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Let A be a 101-element subset of the set S=\{1,2,\ldots,1000000\}. Prove that there exist numbers t_1, t_2, \ldots, t_{100} in S such that the sets A_j=\{x+t_j\mid x\in A\},\qquad j=1,2,\ldots,100 are pairwise disjoint.
Source: Međunarodna matematička olimpijada, shortlist 2003