Strongly symmetric self-orthogonal diagonal Latin squares and Yang Hui type magic squares

In this paper, a strongly symmetric self-orthogonal diagonal Latin square of order n with a special property ( ∗ SSSODLS( n )) is introduced. It is proved that a ∗ SSSODLS( n ) exists if and only if n ≡ 0 ( mod 4 ) and n ≠ 4 . As an application, it is shown that there exists a Yang Hui type magic square YMS ( n , 4 ) if and only if n ≡ 0 ( mod 4 ) and n ≠ 4 .