Question

( 2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)-2^32

Answer 1

$(2 + 1)( {2}^{2} + 1)( {2}^{4} + 1)( {2}^{8} + 1)( {2}^{16} + 1) - {2}^{32}$

$= 3(4 + 1)(16 + 1)(64 + 1)[ {(2}^{8} )^{2} + 1] - ( {2}^{8} )^{4}$

$= 3 \times 5 \times 17 \times 65( {64}^{2} + 1) - {64}^{4}$

$= 16575(4096 + 1) - 16777216$

$= 16575 \times 4097 - 16777216$

$= 67907775 - 16777216$

$= 51130559$