A (v, b, r, k, )-design is called a triple system if k = 3. When k

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.