6

Part of 2000 Czech and Slovak Match

Problems(1)

2 odd integers of same color with difference x,y,x+y,x-y

Source: Czech and Slovak Match 2000 P6

Suppose that every integer has been given one of the colors red, blue, green, yellow. Let

x

y

be odd integers such that

|x| \ne |y|

. Show that there are two integers of the same color whose difference has one of the following values:

x,y,x+y,x-y

Integernumber theorycombinatoricsColoringRamsey Theory