Question

计算：(2+1)(2^2+1)(2^4+1)....(2^32+1)+1

Answer 1

原式子=2^1x(2^2+1)(2^4+1)....(2^32+1)+2^0x(2^2+1)(2^4+1)....(2^32+1)+1 =2^3x(2^4+1)....(2^32+1)+2^2x(2^4+1)....(2^32+1)+2^1x(2^4+1)....(2^32+1)+2^0x(2^4+1)....(2^32+1)+1
=2^7x(2^6+1)....(2^32+1)+2^6x(2^6+1)....(2^32+1)+2^5x(2^6+1)....(2^32+1)+2^4x(2^6+1)....(2^32+1)+......(2^6+1)....(2^32+1)+1
....
=2^31x(2^32+1)+2^30x(2^32+1)+2^29x(2^32+1)+......+2^0x(2^32+1)+1
=2^63+2^62+2^61+2^60+......+2^0+1

Answer 2

(2+1)(2^2+1)(2^4+1)....(2^32+1)
=（闹岁友2-1）液槐(2+1)(2^2+1)(2^4+1)....(2^32+1)+1
=（雀锋2^2-1)(2^2+1)(2^4+1)....(2^32+1)+1
=(2^4-1)(2^4+1)....(2^32+1)+1
=(2^32-1)(2^32+1)+1
=2^64-1+1
=2^64