
(2+1)(2平方+1)(2四次方+1)(2八次方+1)简便计算
2个回答
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利用平方差公式
(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
=65536-1
=65535
(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
=65536-1
=65535
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