Question 32
$A$ is a 20-element set of residue classes modulo $397$. Prove that for any non-negative integer $n$ there exist $x_1, x_2, x_3, x_4 \in A$, such that $x_1 \neq x_2$ and
$$
(x_1 - x_2)n \equiv x_3 - x_4 \pmod{397}
$$
$$
(x_1 - x_2)n \equiv x_3 - x_4 \pmod{397}
$$