Chain Reaction

Algebra Level 3

\[\large (2^{2^0} +1)(2^{2^1} + 1)(2^{2^2} + 1) \cdots (2^{2^{10}} + 1 ) \]

Given that the expression above simplifies to \(2^n - b\), where \(a,b\) and \(n\) are positive integers and \( 0 \leq b < 2^{n-1} \), find \(2+b+n\).

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