2(3+1)(3+1)(3∧4+1)(3∧8+1)…(3∧64+1)+2=
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![2(3+1)(3+1)(3∧4+1)(3∧8+1)…(3∧64+1)+2=](/uploads/image/z/1811055-39-5.jpg?t=2%EF%BC%883%2B1%EF%BC%89%EF%BC%883%2B1%EF%BC%89%EF%BC%883%E2%88%A74%2B1%EF%BC%89%EF%BC%883%E2%88%A78%2B1%EF%BC%89%E2%80%A6%EF%BC%883%E2%88%A764%2B1%EF%BC%89%2B2%3D)
2(3+1)(3+1)(3∧4+1)(3∧8+1)…(3∧64+1)+2=
2(3+1)(3+1)(3∧4+1)(3∧8+1)…(3∧64+1)+2=
2(3+1)(3+1)(3∧4+1)(3∧8+1)…(3∧64+1)+2=
原式
=2(3+1)(3^2+1)(3^4+1)(3^8+1)……(3^64+1)+2
=2(3-1)(3+1)(3^2+1)(3^4+1)(3^8+1)……(3^64+1)/(3-1)+2
=2(3^2-1)(3^2+1)(3^4+1)(3^8+1)……(3^64+1)/2+2
反复用平方差
=2(3^128-1)/2+2
相互抵消
=3^128-1+2
=3^128+1
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