Consider the function $g(x)$ defined as $g(x)\left(x^{\left(2^{2011}-1\right)}-1\right)=(x+1)\left(x^2+1\right)\left(x^4+1\right) \ldots \ldots \ldots . . .\left(x^{2^{2010}}+1\right)-1$, $(|x| \neq 1)$.
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