问题: 22
解答:
(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)/2^32-1
=(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)/[(2^16)^2-1]
=(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)/[(2^16+1)(2^16-1)]
=(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)/[(2^16+1)(2^8+1)(2^8-1)]
=(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)/[(2^16+1)(2^8+1)(2^4+1)(2^4-1)]
=(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)/[(2^16+1)(2^8+1)(2^4+1)(2^2+1)(2^2-1)]
==(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)/[(2^16+1)(2^8+1)(2^4+1)(2^2+1)(2+1)(2-1)]
=1/(2-1)=1
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