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The value of the expression\[(2^{1004}+5^{1005})^2-(2^{1004}-5^{1005})^2\]is $k\cdot10^{1004}$ for some positive integer $k$. What is $k$?

 Jul 28, 2020
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My computer says k = 20. One of the matrhematicians here will give you an algebraic solution.

 Jul 28, 2020

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