# Rotating the Hyperbola

Geometry Level 4

A hyperbola $$H$$ with equation $$xy=n$$ (where $$n\le 1000$$) is rotated $$45^{\circ}$$ to obtain the hyperbola $$H'$$. Let the positive difference between the number of lattice points on $$H$$ and $$H'$$ be $$D$$. Given that both $$H$$ and $$H'$$ have at least one lattice point, find the maximum possible value of $$D$$.

Details and Asumptions: A lattice point is a point that has integer $$x$$- and $$y$$-coordinates.

You may want to look at the list of Highly Composite Numbers.

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