A set of three nonnegative integers with is called historic if . Show that the set of all nonnegative integers can be written as the union of pairwise disjoint historic sets.
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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
Školjka 
with 
is called historic if 
. Show that the set of all nonnegative integers can be written as the union of pairwise disjoint historic sets.