(2+1)(2^2+1)(2^4+1)(2^8+1)如何用平方差公式解?

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(2+1)(2^2+1)(2^4+1)(2^8+1)如何用平方差公式解?
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(2+1)(2^2+1)(2^4+1)(2^8+1)如何用平方差公式解?
(2+1)(2^2+1)(2^4+1)(2^8+1)如何用平方差公式解?

(2+1)(2^2+1)(2^4+1)(2^8+1)如何用平方差公式解?
(2+1)(2^2+1)(2^4+1)(2^8+1)……(2^64+1)+1
=1*(2+1)(2^2+1)(2^4+1)(2^8+1)
=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)
=(2^4-1)(2^4+1)(2^8+1)
=(2^8-1)(2^8+1)
=2^16-1