Why does $-14 \bmod 12 = 10$?
I would be grateful if someone could explain this to me step by step, for I am but a novice in the field of modular arithmetic. [edit] I obtained this equation by playing around with values for (x,y,z) in: x mod y = z on the Google calculator.
Thank you!
Edit: I would like to hit myself on the head- I see it now. Thanks to everyone who responded! Unless there is a discussion going on in this post right now, it can be marked as resolved.
Answer
$-14\equiv10\pmod{12}\,$ because $\,{-}14=10-12\cdot 2$. In other words, $-14$ and $10$ leaves the same remainder after dividing $12.$
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