Cantor Equivalent

Let $R = 990$ be the value of an individual resistor, and $x$ the resistance of the entire circuit. The circuit can be analyzed as consisting of two individual resistors, and two copies of itself: Thus we have $x = R + (x | R | x)$ where $|$ stands for placing elements in parallel. This translates into the algebraic equation $x = R + \frac{1}{\frac 1 x + \frac 1 R + \frac 1 x} \\ \therefore\ \ \ x = R + \frac {R x}{2R + x} \\ \therefore\ \ \ (x - R)(x + 2R) = R x \\ \therefore\ \ \ x^2 - 2R^2 = 0 \\ \therefore\ \ \ x = \sqrt 2 R = \boxed{1400}\ \Omega.$