Suppose that $N$ is an $(\mathcal{F}_{t})$-continuous local martingale, with $N_{0}=1$, $N_{t}\gt0$ a.s. for $t\geq0$ and $N$ satisfies:
$$ N_{t}=1+\lambda\int_{0}^{t} N_{s}dB_{s} $$
Applying Ito's fornula to $F(N_{t})$ for a suitable choice of $F$, show that $N$ is unique.
I'm not really sure where to start with choosing an appropriate $F$. Any help would be much appreciated!