17. A courier company undertakes courier services between 13 cities in a certain area. If each courier can take on the courier services for at most four cities, to ensure that there is at least one courier between every two cities, the courier company needs at least $\qquad$ couriers.
17. 13.

From the problem, we know that there are $\mathrm{C}_{13}^{2}$ types of express delivery services between 13 cities. Each courier can handle at most $\mathrm{C}_{4}^{2}$ types of express delivery services between four cities. Therefore, at least $\frac{\mathrm{C}_{13}^{2}}{\mathrm{C}_{4}^{2}}=13$ couriers are needed.
Below is a construction showing that 13 couriers can meet the requirements:
$$
\begin{array}{l}
1,2,3,4 ; 1,5,6,7 ; 1,8,9,10 ; 1,11,12,13 ; \\
2,5,8,11 ; 2,6,9,12 ; 2,7,10,13 ; \\
3,5,9,13 ; 3,6,10,11 ; 3,7,8,12 ; \\
4,5,10,12 ; 4,6,8,13 ; 4,7,2,11 .
\end{array}
$$