3. The equation $(x-a)(x-8)-1=0$ has two integer roots, then
$$
a=
$$
.
3. 8
Solution: The original equation is rearranged as $x^{2}-(a+8) x+8 a-1=0$.
Let $x_{1}, x_{2}$ be the two integer roots of the equation. From $x_{1}+x_{2}=a+8$, we know that $a$ is an integer, so $x-a$ and $x-8$ are both integers. Therefore, from the original equation, we have
$$
x-a=x-8(= \pm 1) \text {, so } a=8 \text {. }
$$