Question 76
Let $S=\{(x, y) \mid x, y \in \mathbb{Z}, 0 \leq x, y \leq 2016\}$. Given points $A=(x_1, y_1)$, $B=(x_2, y_2)$ in $S$, define
$$
d_{2017}(A, B) = (x_1 - x_2)^2 + (y_1 - y_2)^2 \pmod{2017}
$$
The points $A=(5,5)$, $B=(2,6)$, $C=(7,11)$ all lie in $S$. There is also a point $O \in S$ that satisfies
$$
d_{2017}(O, A) = d_{2017}(O, B) = d_{2017}(O, C)
$$
Find $d_{2017}(O, A)$.
$$
d_{2017}(A, B) = (x_1 - x_2)^2 + (y_1 - y_2)^2 \pmod{2017}
$$
The points $A=(5,5)$, $B=(2,6)$, $C=(7,11)$ all lie in $S$. There is also a point $O \in S$ that satisfies
$$
d_{2017}(O, A) = d_{2017}(O, B) = d_{2017}(O, C)
$$
Find $d_{2017}(O, A)$.