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📰 = 3^4 \cdot 5^2
📰 The number of positive divisors is $ (4+1)(2+1) = 15 $, so there are 15 positive divisor pairs $ (a, b) $ with $ a > 0, b > 0 $, and another 15 with $ a < 0, b < 0 $, giving 30 total integer divisor pairs (since $ a $ and $ b $ can both be negative).
📰 But we only count pairs where $ a $ and $ b $ have the same parity. Since 2025 is odd, all its divisors are odd. Therefore, $ a $ and $ b $ are both odd in every factor pair, and the sum and difference are even. So all 30 pairs yield integer $ (x, y) $.
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