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Each positive divisor \(d\) gives a solution \((d, 100/d)\), and each negative divisor \(-d\) gives \((-d, -100/d)\).
Thus, total lattice points: \(2 \times 9 = 18\) (each positive divisor contributes two points: one in positive quadrant, one in negative).
We verify: for each of the 9 positive \(d\), \((d, 100/d)\) and \((-d, -100/d)\) are distinct lattice points.

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