Bruck-Ryser-Chowla theorem

Meanings

1. A result on the combinatorics of block designs, stating that, if a (v, b, r, k, λ)-design exists with v = b (a symmetric block design), then: (i) if v is even, then k − λ is a square; (ii) if v is odd, then the following Diophantine equation has a nontrivial solution: x² − (k − λ)y² − (−1)^((v−1)/2) λ z² = 0.

Etymology

Named after Richard Bruck, H. J. Ryser, and Sarvadaman Chowla.