IMO Shortlist 1999 problem C6
Dodao/la:
arhiva2. travnja 2012. Suppose that every integer has been given one of the colours red, blue, green or yellow. Let
![x](/media/m/f/1/8/f185adeed9bd346bc960bca0147d7aae.png)
and
![y](/media/m/c/c/0/cc082a07a517ebbe9b72fd580832a939.png)
be odd integers so that
![|x| \neq |y|](/media/m/a/3/3/a33acc06239edd3cc242739156796d42.png)
. Show that there are two integers of the same colour whose difference has one of the following values:
![x,y,x+y](/media/m/3/5/9/3597b8bc4592a790e7ddd0bc06fb9b82.png)
or
![x-y](/media/m/a/f/7/af7fef78d1227c10188c5e0ad1f01014.png)
.
%V0
Suppose that every integer has been given one of the colours red, blue, green or yellow. Let $x$ and $y$ be odd integers so that $|x| \neq |y|$. Show that there are two integers of the same colour whose difference has one of the following values: $x,y,x+y$ or $x-y$.
Izvor: Međunarodna matematička olimpijada, shortlist 1999