KnowraVan der Waerden's theoremLinked fromLinked fromThe 7 pages that link to Van der Waerden's theorem, each with the reason it gives.All 7Related 6Compared with 1Ramsey theoryRelated: It applies the unavoidable-pattern principle to arithmetic progressions.Schur's theoremRelated: It generalizes the search for forced monochromatic patterns beyond a single additive equation.Ramsey's theoremCompared with: It is a neighboring partition theorem with structured progressions as its target.Richard RadoRelated: Rado’s partition-regularity results generalize the kind of unavoidable patterns this theorem establishes.Hales–Jewett theoremRelated: The Hales–Jewett theorem yields this arithmetic-progression result through an encoding.Szemerédi's theoremRelated: It supplied an earlier combinatorial guarantee, while Szemerédi's theorem strengthens it through density.Friends and strangers theoremRelated: It guarantees order in colored numbers rather than uniform relationships among people.