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(2+1)(2^2+1)(2^4+1)(2^6+1)()2^16+1)/2^32-1=
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(2+1)(2^2+1)(2^4+1)(2^6+1)()2^16+1)/2^32-1=
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答案和解析
(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)/(2^32-1)
=(2-1)(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) (平方差公式)
=(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
=(2-1)(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) (平方差公式)
=(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
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