Is 12(mod 13) the same as -1(mod 13)?

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I'm in the process of studying for an exam and this just popped into my head. Sorry if it's a dumb question

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2 Answers

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Yes, they are the same. Note that $(-1)+13=12$, so their difference is exactly the thing that is ignored by mod $13$!

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Indeed they are the same, although I'd write them either without brackets or with brackets around the whole expression.

I really wanted to add that that using the $(-1 \bmod 13)$ representation can be very useful, especially when try to find the result of a multiplication. For a simple example, $12\times 7 \bmod 13$ is easily converted to $12\times 7 \equiv -1\times 7 \equiv -7 \equiv 4 \bmod 13$

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