Consider the curve $y^2 = x^3 + 1$ over the field $F_5$.
Let's add the points $(0, 4)$ and $(4, 0)$.
$\lambda = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 4}{4 - 0} = \frac{-4}{4} = \frac{1}{4} = 1 \cdot 4^{-1} = 1 \cdot 4 = 4$.
$x_3 = \lambda^2 - x_1 - x_2$
$x_3 = 16 - 0 - 4 = 1 - 4 = -3 = 2$
However, there are 2 valid points that have $x = 2$ on $E(F_5)$: $(2, 2), (2,3)$.
How do I know which point is the correct result? The solution says: $(2, 3)$, but doesn't give a reason for one point over the other.
Note: The same ambiguity exists in $(4, 0) + (2, 3)$ on $E(F_5)$.