# Math Help - Number Theory Congruences Proof

1. ## Number Theory Congruences Proof

Hey I'm not really sure how to start out this problem.

We have to prove that if a = b (mod n), then ac = bc (mod n)

How exactly would I prove from a=b to ac = bc for this problem?

2. Hello,
Originally Posted by BlakeRobertsonMD
Hey I'm not really sure how to start out this problem.

We have to prove that if a = b (mod n), then ac = bc (mod n)

How exactly would I prove from a=b to ac = bc for this problem?
You can go to the definition of the congruence :

a=b (mod n) <===> there exists an integer k (positive or negative) such that a-b = kn

so from that, if you multiply by c : ac-bc=kcn. Let k'=cn.
Then ac-bc=k'n <===> ac=bc (mod n)