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 $\qquad$
3.9800 .

By symmetry, we only need to consider the situation above the $x$-axis first.

Let the line $y=k(k=1,2, \cdots, 99)$ intersect the right branch of the hyperbola at point $A_{k}$, and intersect the line $x=100$ at point $B_{k}$. Then the number of integer points inside the segment $A_{k} B_{k}$ is $99-k$. Therefore, the number of integer points in the region above the $x$-axis is
$$
\sum_{k=1}^{9}(99-k)=\sum_{k=0}^{98} k=49 \times 99 \text {. }
$$

There are 98 integer points on the $x$-axis, so the total number of integer points is
$$
2 \times 49 \times 99+98=9800 .
$$