(2+1)(2²+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1
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![(2+1)(2²+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1](/uploads/image/z/1345709-29-9.jpg?t=%EF%BC%882%2B1%EF%BC%89%EF%BC%882%26%23178%3B%2B1%EF%BC%89%EF%BC%882%5E4%2B1%29%282%5E8%2B1%29%282%5E16%2B1%29%282%5E32%2B1%29%2B1)
(2+1)(2²+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1
(2+1)(2²+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1
(2+1)(2²+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+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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=2^64
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(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+...
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(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
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