PL-OM 2016 Problem 5

There are given two positive real number $a<b$ . Show that there exist positive integers $p, \ q, \ r, \ s$ satisfying following conditions: $1$ . $a< \frac{p}{q} < \frac{r}{s} < b$ . $2.$ $p^2+q^2=r^2+s^2$ .