Proof for a higher level math class

[aesailor]

Homework Statement

ac | bc if and only if a | b (Note that this is really two implications.)



2. The attempt at a solution

The only way I can see going about this proof is by using examples. I know that in ac | bc the c will cancel out in both, but I don't know how to properly word the proof. Any suggestions would be greatly helpful.

 

[Mark44]

Homework Statement

ac | bc if and only if a | b (Note that this is really two implications.)



2. The attempt at a solution

The only way I can see going about this proof is by using examples. I know that in ac | bc the c will cancel out in both, but I don't know how to properly word the proof. Any suggestions would be greatly helpful.

You can use examples to disprove a statement (these are called counterexamples), but you can't use examples to prove a statement.

For the direction ac | bc ==> a | b, since ac divides bc, then bc must be some integer multiple of ac, so bc = k * ac, for some integer k. Can you show that this implies that b must be an integer multiple of a?