3B. Find the largest divisor of 1001001001 that is less than 10000.
Solution. Let us note that:

$$
\begin{aligned}
1001001001 & =1001 \cdot 10^{6}+1001=1001 \cdot\left(10^{6}+1\right) \\
& =1001 \cdot\left(10^{2}+1\right) \cdot\left(10^{4}-10^{2}+1\right) \\
& =1001 \cdot 101 \cdot 9901=7 \cdot 11 \cdot 13 \cdot 101 \cdot 9901
\end{aligned}
$$

The number 9901 is prime. It is easily verified that it is the largest divisor of 1001001001 less than 10000.