Interior Lattice Point

Geometry Level 4

An integer lattice point is a point with coordinates (n,m) (n, m) , where nn and mm are integers. As NN ranges from 1 to 905, what is the maximum number of integer lattice points in the interior of a triangle with vertices (0,0), (0,0), (N,907N),(N, 907-N), and (N+1,907N1)?(N+1, 907-N-1)?

Note: The point (0,0) (0,0) is not in the interior of any of the triangles described above.

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