Question 67
Prove that the equation
$$
\frac{1}{\sqrt{x} + \sqrt{1006}} + \frac{1}{\sqrt{2012 - x} + \sqrt{1006}} = \frac{2}{\sqrt{x} + \sqrt{2012 - x}}
$$
has 2013 integer solutions.
$$
\frac{1}{\sqrt{x} + \sqrt{1006}} + \frac{1}{\sqrt{2012 - x} + \sqrt{1006}} = \frac{2}{\sqrt{x} + \sqrt{2012 - x}}
$$
has 2013 integer solutions.