计算:(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)/(2^32-1)
计算:(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)/(2^32-1)=(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)/(...
计算:(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)/(2^32-1)
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)/(2^32-1)
=(2^4-1)(2^4+1)(2^8+1)(2^16+1)/(2^32-1)
=(2^8-1)(2^8+1)(2^16+1)/(2^32-1)
=(2^16-1)(2^16+1)/(2^32-1)
=(2^32-1)(2^32-1)
=1 展开
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)/(2^32-1)
=(2^4-1)(2^4+1)(2^8+1)(2^16+1)/(2^32-1)
=(2^8-1)(2^8+1)(2^16+1)/(2^32-1)
=(2^16-1)(2^16+1)/(2^32-1)
=(2^32-1)(2^32-1)
=1 展开
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2^32-1
= (2^16+1)(2^16-1)
= (2^16+1)(2^8+1)(2^8-1)
= (2^16+1)(2^8+1)(2^4+1)(2^2+1)(2+1)(2-1)
= (2^16+1)(2^8+1)(2^4+1)(2^2+1)(2+1)
代入原式：
(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)/(2^32-1)
＝ (2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)/［(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)］
＝ 1
= (2^16+1)(2^16-1)
= (2^16+1)(2^8+1)(2^8-1)
= (2^16+1)(2^8+1)(2^4+1)(2^2+1)(2+1)(2-1)
= (2^16+1)(2^8+1)(2^4+1)(2^2+1)(2+1)
代入原式：
(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)/(2^32-1)
＝ (2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)/［(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)］
＝ 1
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(2+1)*(2^2+1)*(2^4+1)*(2^8+1)*(2^16+1)/(2^32-1) = 1
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