Question 48
Prove that there exists an infinite set of points
$$
\dots, P_{-3}, P_{-2}, P_{-1}, P_0, P_1, P_2, P_3, \dots
$$
in the plane with the following property: For any three distinct integers $a, b$ and $c$, points $P_a, P_b$ and $P_c$ are collinear if and only if $a + b + c = 2014$.
$$
\dots, P_{-3}, P_{-2}, P_{-1}, P_0, P_1, P_2, P_3, \dots
$$
in the plane with the following property: For any three distinct integers $a, b$ and $c$, points $P_a, P_b$ and $P_c$ are collinear if and only if $a + b + c = 2014$.