van der Waerden's Theorem
For any given Positive Integers 
and 
, there exists a threshold number
(known as a van der Waerden Number) such that no matter how the numbers 1, 2, ..., 
are partitionedinto classes, at least one of the classes contains an Arithmetic Progression of length at least . However, noFormula for is known.
References
Honsberger, R. More Mathematical Morsels. Washington, DC: Math. Assoc. Amer., p. 29, 1991. Khinchin, A. Y. ``Van der Waerden's Theorem on Arithmetic Progressions.'' Ch. 1 in Three Pearls of Number Theory. New York: Dover, pp. 11-17, 1998. van der Waerden, B. L. ``Beweis einer Baudetschen Vermutung.'' Nieuw Arch. Wiskunde 15, 212-216, 1927.
- Wallis Sine Formula
- Wallis's Problem
- Wallpaper Groups
- Walsh Function
- Walsh Index
- Wang's Conjecture
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- Waring Formula
- Waring's Conjecture
- Waring's Prime Conjecture
- Waring's Problem
- Waring's Sum Conjecture
- Waring's Theorem
- Watchman Theorem
- Watson-Nicholson Formula
- Watson Quintuple Product Identity
- Watson's Formula
- Watson's Theorem
- Watt's Curve
- Watt's Parallelogram
- Wave
- Wave Equation
- Wavelet
- Wavelet Matrix
- Wavelet Transform