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$\begin{aligned} \frac{1000^2}{252^2-248^2} &= \frac {1000^2}{(252+248)(252-248)} \\ &= \frac {1000 \cdot 1000}{500 \cdot 4} \\ &= \frac {2 \cdot 1000}{1 \cdot 4} \\ &= \frac {2 \cdot 250}{1 \cdot 1} \\ &= 2 \cdot 250 \\ &= \boxed{500} \end{aligned}$

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