14. Find the number of pairs of positive integers $(x, y)$ which satisfy the equation
$$
20 x+6 y=2006 .
$$
14. Ans: 34
$$
20 x+6 y=2006 \Longleftrightarrow 10 x+3 y=1003 .
$$

The solutions are
$$
(1,331),(4,321),(7,311), \cdots,(94,21),(97,11),(100,1) \text {. }
$$

Thus there are 34 solutions.