MathDB

5

Part of 2016 Dutch Mathematical Olympiad

Problems(1)

Bas has several colours for each of the positive integers, and a few conditions

Source: Dutch NMO 2016 p5

9/7/2019
Bas has coloured each of the positive integers. He had several colours at his disposal. His colouring satis es the following requirements: • each odd integer is coloured blue, • each integer nn has the same colour as 4n4n, • each integer nn has the same colour as at least one of the integers n+2n+2 and n+4n + 4. Prove that Bas has coloured all integers blue.
Coloringcombinatorics