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📰 Each such pair gives a unique $(x,y)$:
📰 We must check for duplicate solutions. But each factor pair $(a,b)$ gives a distinct $(x,y)$, because $a$ and $b$ determine $x$ and $y$ uniquely.
📰 For example, $(a,b)$ and $(b,a)$ would give different $x$ unless $a = b$. But since $a$ and $b$ are interchangeable via the identity, but each ordered pair is counted once. However, in our setup, each ordered pair $(a,b)$ such that $ab = 2025$ is considered. But since $x$ and $y$ depend on $a$ and $b$ linearly, and $a$ ranges over all divisors, including both positions, we must avoid double-counting? No — each ordered pair $(a,b)$ with $ab = 2025$ is distinct and gives one solution.
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