(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1),题没有打完(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1
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![(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1),题没有打完(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1](/uploads/image/z/199942-70-2.jpg?t=%282%5E2%2B1%29%282%5E4%2B1%29%282%5E8%2B1%29%282%5E16%2B1%29%282%5E32%2B1%29%282%5E64%2B1%29%2C%E9%A2%98%E6%B2%A1%E6%9C%89%E6%89%93%E5%AE%8C%282%5E2%2B1%29%282%5E4%2B1%29%282%5E8%2B1%29%282%5E16%2B1%29%282%5E32%2B1%29%282%5E64%2B1%29%2B1)
(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1),题没有打完(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1
(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1),
题没有打完
(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1
(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1),题没有打完(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1
(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1
=(2²-1) (2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1),/3+1
=(2^4-1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1),/3+1
=...
=(2^128-1)/3 +1
先乘以(2²-1),再除以3,保证相等
然后反复应用平方差公式
(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)/(2^2-1)
=(2^4-1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)/(2^2-1)
=(2^8-1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)/(2^2-1)
=...
=(2^128-1)/3
[(2^2-1)× (2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1]/(2^2-1)
=[(2^4-1)2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)]/(2^2-1)
=[(2^8-1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)]/(2^2-1)
=[(2^16-1)(2^16+1)(2^32+1)(2^64+1)]/(2^2-1)
=[(2^32-1)(2^32+1)(2^64+1)]/(2^2-1)
=[(2^64-1)(2^64+1)]/(2^2-1)
=(2^128-1)/3
(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)/(2^2-1)
= (2^4-1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)/(2^2-1)
=(2^8-1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)/(2^2-1)
=………………
=(2^128-1)/(2^2-1)
=1.13^38(或=(2^128-1)/3)
比如用(2^2-1)去乘(2^2+1) 用(2^4-1)去乘(2^4+1)…以此类推,再除掉所乘的数.原理一样,但更容易做(个人认为)