256次根号下((2+1)(2^2+1)(2^4+1)……(2^256+1)+1)

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256次根号下((2+1)(2^2+1)(2^4+1)……(2^256+1)+1)
256次根号下((2+1)(2^2+1)(2^4+1)……(2^256+1)+1)

256次根号下((2+1)(2^2+1)(2^4+1)……(2^256+1)+1)
(2+1)(2^2+1)(2^4+1)……(2^256+1)+1
=(2-1)(2+1)(2^2+1)(2^4+1)……(2^256+1)+1
=(2^2-1)(2^2+1)(2^4+1)……(2^256+1)+1
=(2^4_1)(2^4+1)……(2^256+1)+1
=2^512-1+1=2^512
256次根号下((2+1)(2^2+1)(2^4+1)……(2^256+1)+1)
=2^2=4

(2+1)(2^2+1)(2^4+1)……(2^256+1)+1=﹙2-1﹚(2+1)(2^2+1)(2^4+1)……(2^256+1)+1
=﹙2²-1﹚(2^2+1)(2^4+1)……(2^256+1)+1
=﹙2^4-1﹚(2^4+1)……(2^256+1)+1
=﹙2^256-1﹚(2^256+1)+1
=2^512-1+1
=2^512
256次根号下((2+1)(2^2+1)(2^4+1)……(2^256+1)+1)=256次根号下2^512=4