Question 24
Let $A, B \subseteq \{0, 1, \dots, 2016\}$ be subsets with $|A| = 30$ and $|B| = 31$ elements. Show that there is an integer $n$ such that the set
$$
\{a + nb \pmod{2017} \mid a \in A, b \in B\}
$$
of residues has at least 730 elements.
$$
\{a + nb \pmod{2017} \mid a \in A, b \in B\}
$$
of residues has at least 730 elements.