4

Part of 1988 Czech And Slovak Olympiad IIIA

Problems(1)

2 colors for numbers 1,2,3,..., 2^n

Source: Czech and Slovak Olympiad 1988, National Round, Problem 4

Prove that each of the numbers

1, 2, 3, ..., 2^n

can be written in one of two colors (red and blue) such that no non-constant

2n

-term arithmetic sequence chosen from these numbers is monochromatic .

combinatoricsColoringnumber theoryCombinatorial Number Theory