Bruck-Ryser-Chowla Theorem

The Bruck-Ryser-Chowla theorem is a result in combinatorial design theory giving necessary conditions for the existence of a symmetric block design. Bruck and Ryser proved it for projective planes in 1949 and Chowla and Ryser extended it to general symmetric designs in 1950; it requires that when the design parameter v is even, the quantity k minus lambda must be a perfect square, and when v is odd, a related Diophantine equation must have a nontrivial solution, a condition strong enough to rule out projective planes of orders 6 and 14 even though satisfying it does not by itself guarantee a design exists.