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If I have $a \equiv b \pmod{n}$, it means $n \mid b - a$.

But can you write it as $n \mid a - b$ as well?

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    $a \equiv b \pmod{n} \implies n \mid (a-b) \implies a-b = nk$ for _some_ integer $k$. Can you find an integer $m$ such that $b-a = mn$?2011-12-08
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    Yes, because in $x$ divides $y$ if and only if $\pm x$ divides $\pm y$, and $a-b = -(b-a)$.2011-12-08
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    that would just be -1. but my prof always writes it as b - a2011-12-08

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