An equilateral triangle lies in the plane with two of its vertices at the points (0, 0) and (n, 0), where n is an integer. Determine the number of points (x, y) with integer coordinates that lie in the interior of the triangle.
Your final answer should be a formula that relates the total number of lattice points (x, y), call it N, to the x-coordinate, n. Note also that the lattice points must lie within the triangle and not along its perimeter.
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Send your complete solution by email to firstname.lastname@example.org. This email address shall be removed after the competition closes to avoid spam. This PMQ28 competition closes on MONDAY 22 July at 23:59 GMT - one extra weekday from now on.
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