# When the positive integers are colored, prove there exist three numbers whose sums are all the same color. [closed]

Each positive integer is colored either red, blue and green. Show that there always exists distinct positive integers $$a,b,c$$ such that $$a,b,c,a+b,b+c,a+c,a+b+c$$ are all of the same color.

## closed as off-topic by user26857, zz20s, Xander Henderson, Feng Shao, nmasantaOct 10 at 0:32

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