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Prove that there exists a four-coloring of the set

M = \{1, 2, \cdots, 1987\}

such that any arithmetic progression with

10

terms in the set

M

is not monochromatic.
Alternative formulation
Let

M = \{1, 2, \cdots, 1987\}

. Prove that there is a function

f : M \to \{1, 2, 3, 4\}

that is not constant on every set of

10

terms from

M

that form an arithmetic progression.
Proposed by Romania

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