Question: Let (xi,yi), i = 1,2, ,n, be distinct points with integer coordinates in a two-dimensional plane. What should be the value of n (i.e., how

Let (xi,yi), i = 1,2, ,n, be distinct points with integer coordinates in a two-dimensional plane. What should be the value of n (i.e., how many distinct points are needed) to guarantee that the midpoint of the line joining at least one pair of these points has integer coordinates?

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