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Algebra Level 3

Given the expression \[(1-x)(1+x^{256})(1+x^{16})(1+x^2)(1+x^8)(1+x^{32})(1+x)(1+x^4)(1+x^{128})\]


The above expression can be written as \(\dfrac{1-x^a}{1+x^b}\) such that \(a,b \in \mathbb{N}\) , \(10^2 \leq a \leq 10^3\) and \(10 \leq b \leq 10^2\).

Find the value of \(\sqrt{a+b}\)

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