Question

a divides b then prove that a divides bc for any integer c​

Answer 1

Answer:

The premise “ ac divides bc ” is more conveniently, for this problem, rephrased as “ bc is a multiple of ac ”. (Well, more precisely, “an integral multiple”, but we’ll assume that’s what is meant.) In other words, there exists an integer m such that

bc=acm .

Now divide both sides by c :

b=am .

The last equality says that b is a multiple of a ; i.e., that a divides b .