Question

3(2²+1)(2⁴+1)…(2¹⁶+1)+1

 

Answer 1

=(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)+1

=(2^4-1)(2^4+1)(2^8+1)(2^16+1)+1

=(2^8-1)(2^8+1)(2^16+1)+1

=(2^16-1)(2^16+1)+1

=2^32-1+1

=2^32

Answer 2

\(3\left(2^2+1\right)\left(2^4+1\right)...\left(2^{16}+1\right)+1\)

\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{16}+1\right)+1\)

\(=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)+1\)

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

\(=\left(2^{16}-1\right)\left(2^{16}+1\right)+1\)

\(=\left(2^{32}-1\right)+1\)

\(=2^{32}\)