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I'm sort of stuck on this proof
I know that $a\equiv b\pmod n$ means $a - b = mk$ for some integer $k$
and by the Division algorithm
$a = mq_1 + r_1$
$b = mq_2 + r_2$
$a - b = m(q_1 - q_2) + (r_1 - r_2)$
Once I get to the line above I get stuck how do I show that $r_1 - r_2$ are actually equal and the same remainder? I've looked at other proofs that just say the remainder for $a$ and $b$ equal to $r$.
I feel like i'm missing something extremely obvious.