9. Given the ten-digit number $N=a 2018 b 2019$. Find the values of $a$ and $b$ such that 99 | $N$.

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The translation is provided as requested, maintaining the original formatting and structure.
9. Notice that, $99|N \Leftrightarrow 9| N, 11 \mid N$.

From the problem, we have
$$
\begin{array}{l}
\left\{\begin{array}{l}
a+2+0+1+8+b+2+0+1+9 \\
=a+b+23 \equiv 0(\bmod 9), \\
(a+0+8+2+1)-(2+1+b+0+9) \\
\equiv 0(\bmod 11), \\
0<a \leqslant 9, \\
0 \leqslant b \leqslant 9
\end{array}\right. \\
\Rightarrow\left\{\begin{array}{l}
a+b \equiv 4 \text { or } 13(\bmod 9), \\
a-b \equiv 1(\bmod 11)
\end{array}\right. \\
\Rightarrow a=7, b=6 .
\end{array}
$$