# How Low Can You Go?

Consider an ellipse with the following equation:

$ax^{2}+by^{2}=100$

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.

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