Bruck–Chowla–Ryser theorem

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The Bruck–Chowla–Ryser theorem is a result on the combinatorics of block designs. It states that if a (v, b, r, k, λ)-design exists with v = b (a symmetric design), then:

k − λ is a square

when v is even, and the diophantine equation

x² − (k − λ)y² − (−1)^(v−1)/2 λ z² = 0

has a nontrivial solution when v is odd.

[edit] References

• van Lint, J.H., and R.M. Wilson (1992), A Course in Combinatorics. Cambridge, Eng.: Cambridge University Press.
• Weisstein, Eric W. "Bruck-Ryser-Chowla Theorem." From MathWorld–A Wolfram Web