Question

3(2²+1)(2⁴+1)...(2⁶⁴+1)+1

Answer 1

\(=1\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{64}+1\right)+1\)

\(=\left(2-1\right)\left(2+1\right)\left(2^2+1\right)...\left(2^{64}+1\right)+1\)

\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{64}+1\right)+1\)

\(=\left(2^4-1\right)\left(2^4+1\right)...\left(2^{64}+1\right)+1\)

\(=....\)

\(=\left(2^{64}-1\right)\left(2^{64}+1\right)+1\)

\(=2^{128}-1+1=2^{128}\)