9.3. How many points on the hyperbola $y=\frac{2013}{x}$ have integer coordinates $(x ; y)$?
Answer: 16. Solution. Integer points in the first quadrant correspond to the natural divisors of the number $2013=3 \cdot 11 \cdot 61$. The number of such divisors is 8 (they can be listed directly or the formula $\left(\alpha_{1}+1\right)\left(\alpha_{2}+1\right) \ldots\left(\alpha_{k}+1\right)$ for the number of natural divisors of the number $N=p_{1}{ }^{\alpha_{1}} \cdot p_{2}{ }^{\alpha_{2}} \cdot \ldots \cdot p_{k}{ }^{\alpha_{k}}$ can be used.). Taking into account the symmetric points in the third quadrant, we get the answer.