High Quality Content by WIKIPEDIA articles! The Erdos–Anning theorem states that an infinite number of points in the plane can have mutual integer distances only if all the points lie on a straight line. It is named after Paul Erdos and Norman H. Anning, who proved it in 1945. An alternative way of stating the theorem is that a non-collinear set of points in the plane with integer distances can only be extended by adding finitely many additional points, before no more points can be added. A set of points to which no more can be added, with all points on the integer grid, forms an Erdos-Diophantine graph.

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