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

Question: A (v, b, r, k, )-design is called a triple system if k = 3. When k = 3 and = 1, we call

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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