How Low Can You Go?
Consider an ellipse with the following equation:
How many lattice points within the region \(-1000 \leq x ,y\leq 1000\) cannot lie on any ellipse with real numbers \(a,b\) satisfying \(0<a \leq b \leq 10\)?
Details and Assumptions:
A lattice point is defined as a point with integer coordinates.
\(a\) and \(b\) are not necessarily integers, just real numbers within the constraint.