Prove that if $n$ is large enough, then for each coloring of the subsets of the set $\{1,2,...,n\}$ with $1391$ colors, two non-empty disjoint subsets $A$ and $B$ exist such that $A$, $B$ and $A\cup B$ are of the same color.
Problem
Source: Iran 3rd round 2012-Special Lesson exam-Part 2-P3
Tags: graph theory, combinatorics proposed, combinatorics