已知M=(2+1)(2^2+1)(2^4+1)(2^8+1) ……(2^16
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已知M=(2+1)(2^2+1)(2^4+1)(2^8+1) ……(2^16
已知M=(2+1)(2^2+1)(2^4+1)(2^8+1)
……(2^16+1)(2^128+1)
已知M=(2+1)(2^2+1)(2^4+1)(2^8+1)
……(2^16+1)(2^128+1)
![已知M=(2+1)(2^2+1)(2^4+1)(2^8+1) ……(2^16](/uploads/image/z/11630944-64-4.jpg?t=%E5%B7%B2%E7%9F%A5M%3D%282%2B1%29%282%5E2%2B1%29%282%5E4%2B1%29%282%5E8%2B1%29+%E2%80%A6%E2%80%A6%282%5E16)
答:补一个因数1=2-1,值不变,利用平方差公式:
M=(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1).(2^128+1)
=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1).(2^128+1)
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1).(2^128+1)
=(2^4-1)(2^4+1)(2^8+1)(2^16+1).(2^128+1)
=(2^8-1)(2^8+1)(2^16+1).(2^128+1)
=(2^16-1)(2^16+1).(2^128+1)
=(2^32-1).(2^128+1)
=2^256-1
M=(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1).(2^128+1)
=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1).(2^128+1)
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1).(2^128+1)
=(2^4-1)(2^4+1)(2^8+1)(2^16+1).(2^128+1)
=(2^8-1)(2^8+1)(2^16+1).(2^128+1)
=(2^16-1)(2^16+1).(2^128+1)
=(2^32-1).(2^128+1)
=2^256-1
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