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.
- Resolution Modulus
- Resolvable
- Resolving Tree
- Resonance Overlap
- Resonance Overlap Method
- R-Estimate
- Restricted Divisor Function
- Restricted Growth Function
- Restricted Growth String
- Resultant
- Retardance
- Reuleaux Polygon
- Reuleaux Triangle
- Reversal
- Reverse Greedy Algorithm
- Reverse-Then-Add Sequence
- Reversion of Series
- Reznik's Identity
- Rhodonea
- Rhomb
- Rhombic Dodecahedral Number
- Rhombic Dodecahedron
- Rhombic Icosahedron
- Rhombicosacron
- Rhombicosahedron