Question 3
For a pair of integers $a$ and $b$, with $0 \lt a \lt b \lt 1000$, the set $S \subseteq \{1, 2, \dots, 2003\}$ is called a *skipping set* for $(a, b)$ if for any pair of elements $s_1, s_2 \in S$, $|s_1 - s_2| \notin \{a, b\}$. Let $f(a, b)$ be the maximum size of a skipping set for $(a, b)$. Determine the maximum and minimum values of $f$.