(2+1)(2^2+1)(2^4+1)(2^8+1).(2^2048+1)=?
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/02 19:39:42
![(2+1)(2^2+1)(2^4+1)(2^8+1).(2^2048+1)=?](/uploads/image/z/5555858-50-8.jpg?t=%282%2B1%29%282%5E2%2B1%29%282%5E4%2B1%29%282%5E8%2B1%29.%282%5E2048%2B1%29%3D%3F)
(2+1)(2^2+1)(2^4+1)(2^8+1).(2^2048+1)=?
(2+1)(2^2+1)(2^4+1)(2^8+1).(2^2048+1)=?
(2+1)(2^2+1)(2^4+1)(2^8+1).(2^2048+1)=?
(2+1)(2的平方+1)(2的4次方+1)(2的8次方+1).(2的2048+1)
=(2-1)(2+1)(2的平方+1)(2的4次方+1)(2的8次方+1).(2的2048+1)
=(2的平方-1)(2的平方+1)(2的4次方+1)(2的8次方+1).(2的2048+1)
=.=(2的4096次方-1)
原式=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1).(2^2048+1)
=(2^2-1)(2^2+1))(2^4+1)(2^8+1).(2^2048+1)
然后不停地用平方差公式
=2^4096-1
(2+1)(2^2+1)(2^4+1)(2^8+1)....(2^2048+1)
原式=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)....(2^2048+1)
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)...(2^2048+1)
=(2^4-1)(2^4+1)(2^8+1)...(2^2048+1)
=(2^8-1)(2^...
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(2+1)(2^2+1)(2^4+1)(2^8+1)....(2^2048+1)
原式=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)....(2^2048+1)
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)...(2^2048+1)
=(2^4-1)(2^4+1)(2^8+1)...(2^2048+1)
=(2^8-1)(2^8+1)...(2^2048+1)
=.....
=(2^2048-1)(2^2048+1)
=2^4096-1
用平方差公式
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