A V B R K Design Is Called A Triple

A (v, b, r, k, λ)-design is called a triple system if k = 3. When k = 3 and λ = 1, we call the design a Steiner triple system.
(a) Prove that in every triple system, λ(v – 1) is even and λv(v – 1) is divisible by 6.
(b) Prove that in every Steiner triple system, v is congruent to 1 or 3 modulo 6.

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