Title says it all. Google doesn't have anything. Trying to get it to let me submit by typing more words. There is nothing really to be added but it wont let me submit without this.
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$\begingroup$If you ignore the meaning of $ -1 $ and consider it an arbitrary symbol, what properties does it have? By definition, it is the value such that $(-1) + 1 = 0$.
But, working mod 3, $2+1= 3 \equiv 0.$ But from earlier, we have $0 = (-1) + 1$. If you combine the two into $2+1 \equiv (-1)+1 \mod 3$ and drop the $+1$ from both sides, you get $2 \equiv -1 \mod 3$.
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