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IMO ShortList 2001, combinatorics problem 4

Source: IMO ShortList 2001, combinatorics problem 4

September 30, 2004

combinatoricsCombinatorial Number TheorypartitionColoringIMO Shortlist

Problem Statement

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.