一道巧算问题(2+1)(2^2+1)(2^4+1)(2^8+1)+1

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一道巧算问题(2+1)(2^2+1)(2^4+1)(2^8+1)+1

一道巧算问题(2+1)(2^2+1)(2^4+1)(2^8+1)+1
一道巧算问题
(2+1)(2^2+1)(2^4+1)(2^8+1)+1

一道巧算问题(2+1)(2^2+1)(2^4+1)(2^8+1)+1
原式=(2-1)*[(2+1)*(2^2+1)*(2^4+1)*(2^8+1)+1]/(2-1)
=[(2-1)*(2+1)*(2^2+1)*(2^4+1)*(2^8+1)+(2-1)*1]/1
=(2^2-1)*(2^2+1)*(2^4+1)*(2^8+1)+1
=(2^4-1)*(2^4+1)*(2^8+1)+1
=(2^8-1)*(2^8+1)+1
=2^16-1+1
=65536