"van der Waerden's theorem" meaning in English

{
  "etymology_text": "Named after the Dutch mathematician B. L. van der Waerden.",
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      "glosses": [
        "In Ramsey theory, a theorem stating 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 whose elements are of the same color."
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          "arithmetic progression",
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        "(mathematics) In Ramsey theory, a theorem stating 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 whose elements are of the same color."
      ],
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  "word": "van der Waerden's theorem"
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{
  "etymology_text": "Named after the Dutch mathematician B. L. van der Waerden.",
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        "In Ramsey theory, a theorem stating 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 whose elements are of the same color."
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        "(mathematics) In Ramsey theory, a theorem stating 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 whose elements are of the same color."
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