4. Find a factor of 1464101210001 , such that it lies between 1210000 and 1220000 .求 1464101210001 在 1210000 和 1220000 之間的一個因數。
4. 1211101
4. Note that $14641=11^{4}$ and $121=11^{2}$. Hence
$$
\begin{aligned}
1464101210001 & =14641 \times 10^{8}+121 \times 10^{4}+1 \\
& =1100^{4}+1100^{2}+1 \\
& =1100^{4}+2 \times 1100^{2}+1-1100^{2} \\
& =\left(1100^{2}+1\right)^{2}-1100^{2} \\
& =\left(1100^{2}+1+1100\right)\left(1100^{2}+1-1100\right) \\
& =1211101 \times 1208901
\end{aligned}
$$
and so 1211101 is a possible answer.
Remark. It can be checked that the answer is unique.