2014 USAMO Problems/Problem 3
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Problem
Prove that there exists an infinite set of points ![\[\ldots,\,\,\,\,P_{-3},\,\,\,\,P_{-2},\,\,\,\,P_{-1},\,\,\,\,P_0,\,\,\,\,P_1,\,\,\,\,P_2,\,\,\,\,P_3,\,\,\,\,\ldots\]](http://latex.artofproblemsolving.com/5/b/1/5b1a20529975d46579986b86a5706fa36bda7794.png)
in the plane with the following property: For any three distinct integers 
and 
, points 
, 
, and 
are collinear if and only if 
.
