PL-OM 1983 Problem 2

Let be given an irrational number $a$ in the interval $(0,1)$ and a positive integer $N$ . Prove that there exist positive integers $p,q,r,s$ such that $\frac{p}{q} < a <\frac{r}{s}, \frac{r}{s} -\frac{p}{q}<\frac{1}{N}$ , and $rq- ps = 1$ .