Question

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

Answer 1

True.

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.