
(2的二次方+1)(2的四次方+1)(2的八次方+1)……(2的三十二方+1)
2个回答
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(2^2+1)(2^4+1)(2^8+1)×...×(2^32+1)
=(2^-1)(2^2+1)(2^4+1)(2^8+1)×...×(2^32+1)×1/3
=(2^4-1)(2^4+1)(2^8+1)×...×(2^32+1)×1/3
=(2^8-1)(2^8+1)×...×(2^32+1)×1/3
.......
=(2^64-1)/3.
方法用平方差公式:(a+1)(a-1)=a²-1,
=(2^-1)(2^2+1)(2^4+1)(2^8+1)×...×(2^32+1)×1/3
=(2^4-1)(2^4+1)(2^8+1)×...×(2^32+1)×1/3
=(2^8-1)(2^8+1)×...×(2^32+1)×1/3
.......
=(2^64-1)/3.
方法用平方差公式:(a+1)(a-1)=a²-1,
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