MathDB
Existence of lattice points on circle

Source:

October 31, 2010
geometrycircumcircleanalytic geometrymodular arithmeticgeometry unsolved

Problem Statement

Let C\mathcal{C} be the circumcircle of the square with vertices (0,0),(0,1978),(1978,0),(1978,1978)(0, 0), (0, 1978), (1978, 0), (1978, 1978) in the Cartesian plane. Prove that C\mathcal{C} contains no other point for which both coordinates are integers.