High Quality Content by WIKIPEDIA articles! Van der Waerden's theorem is a theorem in the branch of mathematics called Ramsey theory. The theorem is about the basic structure of the integers. It is named after the Dutch mathematician B. L. van der Waerden. Van der Waerden's theorem states that for any given positive integers r and k, there is some number N such that if the integers {1, 2, ..., N} are colored, each with one of r different colors, then there are at least k integers in arithmetic progression all of the same color. The least such N is the Van der Waerden number W(r, k).

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