Prove that If a ≡ b (mod n) and c > 0, then ca ≡ cb (mod cn).
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Originally Posted by porterhv Prove that If a ≡ b (mod n) and c > 0, then ca ≡ cb (mod cn). $\displaystyle a \equiv b (\bmod n) \Leftrightarrow \exists k \in \mathbb{Z} \text{ such that } a-b=kn$ $\displaystyle \implies ca-cb=ckn$ $\displaystyle \implies ca-cb=k(cn)$ $\displaystyle \implies ca \equiv cb (\bmod{cn})$ Edit : hey ! that's my 34th ^^
Last edited by Moo; Sep 29th 2008 at 11:29 AM.
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