5. How many solutions in integers does the equation $x^{2}+y^{2}=6 x+2 y+15$ have?

ANSWER: 12.
Solution: By completing the square, we obtain the equation of the circle $(x-3)^{2}+$ $(y-1)^{2}=25$. This is possible when one of the terms equals 25 and the other equals 0 (4 cases), or when one equals 16 and the other equals 9 (8 cases).