Question

Thực hiện phép tính:
(2+1)(2²+1)(2⁴+1)...(2²⁵⁶+1)

Answer 1

\(=\left(2^2-1\right)\left(2^2+1\right)\cdot...\cdot\left(2^{256}+1\right)\)

\(=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\cdot...\cdot\left(2^{256}+1\right)\)

\(=\left(2^8-1\right)\left(2^8+1\right)\cdot\left(2^{16}+1\right)\cdot...\cdot\left(2^{256}+1\right)\)

\(=\left(2^{16}-1\right)\left(2^{16}+1\right)\cdot\left(2^{32}+1\right)\cdot...\cdot\left(2^{256}+1\right)\)

\(=2^{512}-1\)