3. The number of lattice points (points with integer coordinates) inside the region (excluding the boundary) bounded by the right branch of the hyperbola $x^{2}-y^{2}=1$ and the line $x=100$ is $\qquad$ .
Since $y^{2}=x^{2}-1$, when $x=2$, $y=-1,0,1$ for a total of 3 integer points; when $x=3$, $y=-2,-1,0,1,2$ for a total of 5 integer points; $\qquad$ when $x=99$, $y=-98,-97, \cdots, 97,98$ for a total of 197 integer points. Therefore, the number of integer points inside the region is $\frac{98(3+197)}{2}=9800$.