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AoPS Wiki:Problem of the Day/September 6, 2011

The integers $a,b,c,d$ satisfy $a > b > c > d$ and \[a + b + c + d = 2048 \ \textrm{ and }\ a^2 - b^2 + c^2 - d^2 = 2048.\] Find the smallest possible value of $a$.

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