Prove that for a, b, c E ℤ, if a ❘ (ab + c), then a I c.

True.

Step-by-step explanation:

Let a, b, c integers and a | (ab+c), that is to say that there exist a integer k such that ab+c = ka. Then:

ab+c = ka

c = ka-ab

c = a (k-b). So, c is a multiple of a, that is a | c.