# Congruence Proof

• September 29th 2008, 11:00 AM
porterhv
Congruence Proof
Prove that If a ≡ b (mod n) and c > 0, then ca ≡ cb (mod cn).
• September 29th 2008, 11:02 AM
Moo
Quote:

Originally Posted by porterhv
Prove that If a ≡ b (mod n) and c > 0, then ca ≡ cb (mod cn).

$a \equiv b (\bmod n) \Leftrightarrow \exists k \in \mathbb{Z} \text{ such that } a-b=kn$

$\implies ca-cb=ckn$

$\implies ca-cb=k(cn)$

$\implies ca \equiv cb (\bmod{cn})$

Edit : hey ! that's my 34:):)th ^^