6. In the Cartesian coordinate plane, the number of integer points (i.e., points with both coordinates as integers) on the circumference of a circle centered at $(199,0)$ with a radius of 199 is $\qquad$ .
6. 4 .

Let $A(x, y)$ be an integer point on circle $O$. As shown in the figure, the equation of circle $O$ is $y^{2}+(x-199)^{2}=$ $199^{2}$.
$$
\begin{array}{l}
\text { Clearly, } x=0, y=0 ; \\
x=199, y=199 ; \\
x=199, y=-199 ; x=389, y=0
\end{array}
$$

These are 4 solutions to the equation. However, when $y \neq 0, \pm 199$, $y$ is coprime with 199, so 199 can be expressed as the sum of the squares of two positive integers, i.e., $199=m^{2}+n^{2}$. Since $199=4 \times 49+3$, we can set $m=2 k, n=2 l+1$, then.
$$
199=4 k^{2}+4 l^{2}+4 l+1=4\left(k^{2}+l^{2}+l\right)+1 .
$$
The integer points are:
$$
(0,0),(199,199),(389,0),(199,-199) \text {. }
$$