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Dividing a square into (n-1)^2 congruent squares

Source: IMO LongList 1970 - P53

May 22, 2011
conicsparabolaanalytic geometryarithmetic sequencecombinatorics unsolvedcombinatorics

Problem Statement

A square ABCDABCD is divided into (nāˆ’1)2(n - 1)^2 congruent squares, with sides parallel to the sides of the given square. Consider the grid of all n2n^2 corners obtained in this manner. Determine all integers nn 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 nn points of the grid.
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