Proved in 1933. If is an Odd Prime or and is any Positive Integer, then there is a
Hadamard Matrix of order

where is any Positive Integer such that . If is of this form, the matrix can be constructed with 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 .

© 1996-9

1999-05-26