IMO 1984 LL GDR30

Decide whether it is possible to color the 1984 natural numbers

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IMO 1984 LL GDR30

Origin: GDR

Problem

Decide whether it is possible to color the 1984 natural numbers 1, 2, 3, . . ., 1984 using 15 colors so that no geometric sequence of length 3 of the same color exists.