IMO Shortlist 2001 problem C4


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2. travnja 2012.
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A set of three nonnegative integers \{x,y,z\} with x < y < z is called historic if \{z-y,y-x\} = \{1776,2001\}. Show that the set of all nonnegative integers can be written as the union of pairwise disjoint historic sets.
Izvor: Međunarodna matematička olimpijada, shortlist 2001