Hi I was soliving Elliptic Curves and I found out $2P$ but when it came to $3P$ I became a little bit stumped. My equation is $$y^2 =x^3 + 2x + 9 \qquad(\text{mod } 23)\ .$$ The values I got for $P$ is $(0,3)$ and $2P$ is $(18,14)$, I do know that when $P\ne Q$ the equation to find the slope for $R$ is $$\frac{(y_2 - y_1)}{(x_2-x_1)}\qquad (\text{mod } 23)\ .$$ However when I try to find the slope I get a decimal number, not sure if I'm missing a step or if I'm supposed to continue as is.
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See Quick beginner guide for asking a well-received question – Lucky Chouhan Nov 06 '23 at 04:11
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3The computations should be done in the field $F$ with $23$ elements, so the slope is$$\frac{14-3}{18-0}=11\cdot 9=99=7\ .$$Here, the multiplicative inverse of $18$ is $9$ because $18\cdot 9 = 162=161+1=7\cdot 23 +1=7\cdot 0+1=0+1=1$. – dan_fulea Nov 06 '23 at 13:26