Paley's Theorem
Proved in 1933. If 
is an Odd Prime or 
and 
is any Positive Integer, then there is aHadamard Matrix of order
where
is any Positive Integer such that 
. If 
is of this form, the matrix can be constructedwith a Paley Construction. If is divisible by 4 but not of the form (1), the Paley Class is undefined.However, Hadamard Matrices have been shown to exist for all for 
.See also Hadamard Matrix, Paley Class, Paley Construction- B-Tree
- Bubble
- Buchberger's Algorithm
- Buckminster Fuller Dome
- Buffon-Laplace Needle Problem
- Buffon's Needle Problem
- Bulirsch-Stoer Algorithm
- Bullet Nose
- Bumping Algorithm
- Bundle
- Burau Representation
- Burkhardt Quartic
- Burnside Problem
- Burnside's Conjecture
- Burnside's Lemma
- Busemann-Petty Problem
- Busy Beaver
- Small Multiple Method
- Small Number
- Small Retrosnub Icosicosidodecahedron
- Small Rhombicosidodecahedron
- Small Rhombicuboctahedron
- Small Rhombidodecacron
- Small Rhombidodecahedron
- Small Rhombihexacron