(3+1)(3²+1)(3的四次方+1)(3的八次方+1)...(3的十次方+1)
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![(3+1)(3²+1)(3的四次方+1)(3的八次方+1)...(3的十次方+1)](/uploads/image/z/575731-19-1.jpg?t=%EF%BC%883%2B1%EF%BC%89%EF%BC%883%26%23178%3B%2B1%EF%BC%89%EF%BC%883%E7%9A%84%E5%9B%9B%E6%AC%A1%E6%96%B9%2B1%EF%BC%89%EF%BC%883%E7%9A%84%E5%85%AB%E6%AC%A1%E6%96%B9%2B1%EF%BC%89...%EF%BC%883%E7%9A%84%E5%8D%81%E6%AC%A1%E6%96%B9%2B1%EF%BC%89)
(3+1)(3²+1)(3的四次方+1)(3的八次方+1)...(3的十次方+1)
(3+1)(3²+1)(3的四次方+1)(3的八次方+1)...(3的十次方+1)
(3+1)(3²+1)(3的四次方+1)(3的八次方+1)...(3的十次方+1)
原式通过乘上1/2×(3-1),可以不断的形成平方差.
原式
=1/2×(3-1)(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)
=1/2×(3^2-1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)
=1/2×(3^4-1)(3^4+1)(3^8+1)(3^16+1)
=1/2×(3^8-1)(3^8+1)(3^16+1)
=1/2×(3^16-1)(3^16+1)
=1/2×(3^32-1)