Suppose that every integer has been given one of the colours red, blue, green or yellow. Let and be odd integers so that . Show that there are two integers of the same colour whose difference has one of the following values: or .
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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 $x-y$.
Source: Međunarodna matematička olimpijada, shortlist 1999
Školjka 
and 
be odd integers so that 
. Show that there are two integers of the same colour whose difference has one of the following values: 
or 
.