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

分类: 作业答案 • 2022-05-20 18:34:33
问题描述：

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

答

令A=上式,则
(2-1)A
=(2^2-1)(2^2+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
A=2^64

答

(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
=2^64-1+1=2^64

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