(i) Find a solution in integers of the Pell equation $x^{2}-17 y^{2}=1$.

(ii) Define the continued fraction expansion of a real number $\theta>1$ and show that it converges to $\theta$.

Show that if $N>0$ is a nonsquare integer and $x$ and $y$ are integer solutions of $x^{2}-N y^{2}=1$, then $x / y$ is a convergent of $\sqrt{N}$.