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- Multiplicative Persistence
- Multiplicative Primitive Residue Class Group
- Multiplicity
- Multiplier
- Multiply Connected
- Multiply Perfect Number
- Multisection
- Multivalued Function
- Multivariate Analysis
- Multivariate Function
- Multivariate Theorem
- Mu Molecule
- Mutant Knot
- Mutation
- Mutual Energy
- Mutually Exclusive
- Mutually Singular
- Myriad
- Myriagon
- Mystic Pentagram
- Méiré Pattern
- Ménage Number
- Ménage Problem
- Möbius Band
- Möbius Function