HELP pleeeeeeeeeeeeeeeeeease!!!!11111?

Question

the whole page is colored with 3 colors . prove that
in the set of one of these colors we have all the distences(natural numbers)?


sorry if it is not clear, i have translated it from my own language.


if you got the question please explain easily so that i understand.
thank you.

Answer 1

I'm not remembering the proof immediately, but this is a famous "Ramsey coloring" problem. You might want to search on that phrase.