(2+1)(2的平方+1)(2的^4+1)(2的^8+1)·····一直乘到2^2n 次方
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(2+1)(2^2+1)(2^4+1)(2^8+1)····· (2^2n+1)
= (2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)····· (2^2n+1)
= (2^2-1)(2^2+1)(2^4+1)(2^8+1)····· (2^2n+1)
= (2^4-1)(2^4+1)(2^8+1)····· (2^2n+1)
= (2^8-1)(2^8+1)····· (2^2n+1)
= (2^16-1)····· (2^2n+1)
= 2^4n-1
= (2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)····· (2^2n+1)
= (2^2-1)(2^2+1)(2^4+1)(2^8+1)····· (2^2n+1)
= (2^4-1)(2^4+1)(2^8+1)····· (2^2n+1)
= (2^8-1)(2^8+1)····· (2^2n+1)
= (2^16-1)····· (2^2n+1)
= 2^4n-1
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