# 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 $$2+b+n$$.

×