Bruck–Ryser–Chowla theorem

The Bruck-Chowla-Ryser theorem is a result on the combinatorics of designs. It states that if a (v; k; )- design exists, then:

k −  is a square,

when v is even; and the diophantine equation

x² − (k − )y² − (−1)^(v−1)/2 = z²

has a nontrivial solution, when v is odd.