Question

急，30分，一道数学，快，(2^2+1)(2^4+1)(2^8+1)(2^16+1)

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Answer 1

(2^2+1)(2^4+1)(2^8+1)(2^16+1)
=(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)*1/3
=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)*1/3

=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)*1/3

=(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)*1/3

=(2^4-1)(2^4+1)(2^8+1)(2^16+1)*1/3

=(2^8-1)(2^8+1)(2^16+1)*1/3

==(2^16-1)(2^16+1)*1/3

=(2^32-1)*1/3

Answer 2

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

Answer 3

5*17*257*65537
=1431655765

Answer 4

解：
原式=(2²-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)/(2²-1)
=(2^4-1)(2^4+1)(2^8+1)(2^16+1)/3
=(2^8-1)(2^8+1)(2^16+1)/3
=(2^16-1)(2^16+1)/3
=(2^32-1)/3

Answer 5

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