IMO Shortlist 2001 problem C4
Dodao/la:
arhiva2. travnja 2012. A set of three nonnegative integers
![\{x,y,z\}](/media/m/8/4/d/84d23a60f06e9df180c37e977b0fe06a.png)
with
![x < y < z](/media/m/f/8/2/f8230ecd7f3fe97f52c4f0ed42914597.png)
is called historic if
![\{z-y,y-x\} = \{1776,2001\}](/media/m/2/7/8/2787dd91144384f7d46d59375c908c4c.png)
. Show that the set of all nonnegative integers can be written as the union of pairwise disjoint historic sets.
%V0
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