Adding points of an elliptic curve over a finite field

Question

I'm a bit confused with how fractions are handled with adding points of elliptic curves over finite fields. Below is an example from the text which I am trying to understand:

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The part that particularly confuses me is

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If I think about this the same way that $1/5$ was handled, we have that $246/1 = 246\cdot1^{-1}=246\cdot1=246$, but $246\equiv12 \mod 13$ so shouldn't $246/1 = 12$? I don't understand how the calculation is being done. Could someone explain?

@anon http://math.stackexchange.com/questions/430836/doubling-a-point-on-an-elliptic-curve?rq=1 referring to this post my calculation seems to make sense, so you are probably right — Alex, Jul 22 '13 at 06:43

score 3 · Accepted Answer · answered Jul 22 '13 at 06:42

3

You are right. The text is just missing a minus sign. The answer is $$\lambda \equiv 12 \equiv -1 \mod 13.$$

answered Jul 22 '13 at 06:42

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Adding points of an elliptic curve over a finite field

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