Problem

Source: Iran 3rd round 2012-Special Lesson exam-Part 2-P2

Tags: function, probability, arithmetic sequence, combinatorics proposed, combinatorics



Suppose W(k,2) is the smallest number such that if nW(k,2), for each coloring of the set {1,2,...,n} with two colors there exists a monochromatic arithmetic progression of length k. Prove that W(k,2)=Ω(2k2).