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Let $ a = x - y $ and $ b = x + y $, so $ ab = 2025 $. Since $ x $ and $ y $ are integers, $ a $ and $ b $ must both be integers, and both must be either even or odd to ensure $ x =
The number of positive divisors is $ (4+1)(2+1) = 15 $. So there are 15 positive divisor pairs $ (a, b) $ with $ ab = 2025 $. Including negative divisors, we have $ 30 $ total integer pairs $ (a, b) $.
But we must ensure $ a $ and $ b $ are both odd. Note that $ 2025 $ is odd, so all its divisors are odd. Hence $ a $ and $ b $ are both odd, so $ a + b $ and $ b - a $ are even, and $ x, y $ are integers. Therefore, every divisor pair yields a lattice point.

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