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 .
See also Hadamard Matrix, Paley Class, Paley Construction
© 1996-9 Eric W. Weisstein
1999-05-26