Williamson conjecture
In combinatorial mathematics, specifically in combinatorial design theory and combinatorial matrix theory, the Williamson conjecture is that Williamson matrices of order n {\displaystyle n} exist for all positive integers n {\displaystyle n} . Four symmetric and circulant matrices A {\displaystyle A} , B {\displaystyle B} , C {\displaystyle C} , D {\displaystyle D} are called Williamson matrices if their entries are ± 1 {\displaystyle \pm 1} and they satisfy the relationship A 2 + B 2 + C 2 + D 2 = 4 n I {\displaystyle A^{2}+B^{2}+C^{2}+D^{2}=4n\,I} where I {\displaystyle I} is the identity matrix of order n {\displaystyle n} .