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Colouring natural numbers using 15 colours

Source:

October 11, 2010
geometric sequencenumber theory unsolvednumber theory

Problem Statement

Decide whether it is possible to color the 19841984 natural numbers 1,2,3,,19841, 2, 3, \cdots, 1984 using 1515 colors so that no geometric sequence of length 33 of the same color exists.