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IMO ShortList 1999, combinatorics problem 6

Source: IMO ShortList 1999, combinatorics problem 6

November 14, 2004
functionlinear algebracombinatoricsIMO ShortlistRamsey Theory

Problem Statement

Suppose that every integer has been given one of the colours red, blue, green or yellow. Let xx and yy be odd integers so that ∣x∣≠∣y∣|x| \neq |y|. Show that there are two integers of the same colour whose difference has one of the following values: x,y,x+yx,y,x+y or x−yx-y.
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