inverse problem about scalar multiplication on elliptic curve Let $E$ be an elliptic curve over a finite field $F_p$. Given $n$ be a positive integer and $Q$ be a point on $E$, assume that $Q=nP$, how can we find this $P$? We can assume that $n|p-1$. If $n$ is "small", I would imagine that it is possible using division polynomials. Is it a difficult problem if $n$ is large enough? How difficult is it?
As Samuel Neves described in the comments it is trivially possible to obtain $P$ from $Q=[n]P$, given $Q$ and the integer $n$.

Simply compute $k=n^{-1} \bmod \ell$, with $\ell=|E(\mathbb F_p)|$ being the order (= the number of points) of the curve. $\ell$ is usually known.

Then, to obtain the desired point $P$, calculate $P=[k]Q=[kn]P$ and you're done.