Properties of Divisibility

Question

Let a, b, and c be integers with a≠0. Prove that if a|b and b|c then a|c.

Answer 1

Since a l b, b = k₁a for some integer k₁

 

Since b l c, c = k₂b, for some integer k₂

 

So, c = k₂b

 

        = k₂(k₁a) = (k₂k₁)a   Since k₁ and k₂ are integers, so is k₁k₂

 

Therefore, a l c