Does $P_1+P_2+P_3=2Q$ where $\{P_i\}_{i=1}^3,Q\in E(\Bbb F_p)$ for an ellliptic curve $E/\Bbb F_p$ mean $Q\in\{P_i\}_{i=1}^3$?
I think I could just ask does $P_1+P_2=2Q$ where $\{P_i\}_{i=1}^2,Q\in E(\Bbb F_p)$ for an ellliptic curve $E/\Bbb F_p$ mean $Q=P_1=P_2$?
The answer is likely no.
Just curious.
No. For example, if $Q=0$, then you can definitely find 2 (or 3) nonzero points that add up to 0.