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2013 integer solutions for radical equation 2013 Romania District VII p1

Source:

September 1, 2024
algebradiophantine

Problem Statement

Prove that the equation 1x+1006+12012−x+1006=2x+2012−x\frac{1}{\sqrt{x} +\sqrt{1006}}+\frac{1}{\sqrt{2012 -x} +\sqrt{1006}}=\frac{2}{\sqrt{x} +\sqrt{2012 -x}} has 20132013 integer solutions.
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