A square ABCD is divided into (nā1)2 congruent squares, with sides parallel to the sides of the given square. Consider the grid of all n2 corners obtained in this manner. Determine all integers n for which it is possible to construct a non-degenerate parabola with its axis parallel to one side of the square and that passes through exactly n points of the grid. conicsparabolaanalytic geometryarithmetic sequencecombinatorics unsolvedcombinatorics