I understand that $a \equiv b \pmod n$ means when you divide each $a$ and $b$ by $n$ you get the same remainder. But why do people say: "$a$ divided by $n$ gives you remainder $b$"?
They say that in the first 30 seconds of this video lecture http://www.youtube.com/watch?v=QXIlkq06Ct0&feature=youtube_gdata_player
$12 \equiv 17 \pmod 5$
$12$ divided $5$ has remainder of $2$
17 divided by 5 has remainder of 2
Neither has the latter relation, so why do people sometimes say this.