Question

（2+1）（2²+1）（2^4+1)(2^8+1)(2^16+1)(2^32+1)+1

Answer 1

因为(2-1)=1
所以可以给原式乘上(2-1)，原式的值不变
原式=(2-1)(2+1)(2²+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1
=(2²-1)(2²+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1
=(2^4-1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1
=(2^8-1)(2^8+1)(2^16+1)(2^32+1)+1
=(2^16-1)(2^16+1)(2^32+1)+1
=(2^32-1)(2^32+1)+1
=2^64-1+1
=2^64

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Answer 2

=2^64
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Answer 3

（2+1）（2²+1）（2^4+1)(2^8+1)(2^16+1)(2^32+1)+1
=(2-1)（2+1）（2²+1）（2^4+1)(2^8+1)(2^16+1)(2^32+1)+1
=(2²-1)（2²+1）（2^4+1)(2^8+1)(2^16+1)(2^32+1)+1
=（2^4-1）（2^4+1)(2^8+1)(2^16+1)(2^32+1)+1
=（2^8-1)(2^8+1)(2^16+1)(2^32+1)+1
=(2^16-1)(2^16+1)(2^32+1)+1
=(2^32-1)(2^32+1)+1
=(2^64-1)+1
=2^64