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Now list all factor pairs of 36 (positive and negative):

Now ( -6, -6 ) gives (-6,0), already.

So only 6 factor pairs with both even.

Are there more? What about ( -6, 0 ) and (6,0) — yes.

Is ( -10, -8 ) different from ( -10, 8 )? Yes.

So the number of lattice points is 6.

But double-check symmetry: hyperbola is symmetric over both axes and origin. So if (10,8) is on it, so are (10,-8), (-10,8), (-10,-8) — four points from this solution pair.

Then (6,0), (-6,0) are on x-axis — two points.

Squares mod 8: possible values are 0,1,4.

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