(i) Let $M$ and $N$ be positive integers, such that $N$ is not a perfect square. If $M<\sqrt{N}$, show that every solution of the equation

$$x^{2}-N y^{2}=M$$

in positive integers $x, y$ comes from some convergent of the continued fraction of $\sqrt{N}$.

(ii) Find a solution in positive integers $x, y$ of

$$x^{2}-29 y^{2}=5$$