Rotating the Hyperbola

Geometry Level 4

A hyperbola HH with equation xy=nxy=n (where n1000n\le 1000) is rotated 4545^{\circ} to obtain the hyperbola HH'. Let the positive difference between the number of lattice points on HH and HH' be DD. Given that both HH and HH' have at least one lattice point, find the maximum possible value of DD.

Details and Asumptions: A lattice point is a point that has integer xx- and yy-coordinates.

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

×

Problem Loading...

Note Loading...

Set Loading...