van der Waerden's theorem
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van der Waerden's theorem[¦van ·dər ′werd·ənz ‚thir·əm]
The theorem that for any positive integers k and r there is a positive integer n such that, if the first n integers are divided into k classes, then there exists an arithmetic progression of r terms that all belong to the same class.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.