(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+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)(3^32+1)
=1/2×(3^2-1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)
=1/2×(3^4-1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)
=1/2×(3^8-1)(3^8+1)(3^16+1)(3^32+1)
=1/2×(3^16-1)(3^16+1)(3^32+1)
=1/2×(3^32-1)(3^32+1)
=1/2×(3^64-1)
=(3^64-1)/2