3 . Find the integers $x, y$ that satisfy the equation $2 x-3 y=17$, and for which $x^{2}+y^{2}$ is minimized, as well as the minimum value of $x^{2}+y^{2}$.
3. Answer: $x=4, y=-3, x^{2}+y^{2}$ has a minimum value of 25.
Hint: The general solution of $2 x-3 y=17$ is $x=3 t+7$, $y=2 t-1$. Substituting into $x^{2}+y^{2}$, we get $x^{2}+y^{2}$ $=13\left(t+\frac{19}{13}\right)^{2}+\frac{289}{13}$. The integer $t$ closest to $t=-\frac{19}{13}$ is -1.