Problem no. 7

If \((2+1)(2^2+1)(2^{2^2}+1)(2^{2^3}+1)(2^{2^4}+1)\dots (2^{2^{99}}+1)=2^a+b\), where \(a\) and \(b\) are integers.

Find the value of \(2a-b\).

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