Properties of Divisibility

Question

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

Answer 1

When I was looking around the internet, the proofs I saw used a|bc instead. Double-check that this is OK for answer. The proof:

 

The notation a|b means that an = b, where n is an integer. Multiply both sides by c

 

acn = bc

 

Since c and n are integers, the product will be an integer (call it m). Thus

 

am = bc

 

This shows that a|bc.