(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)等于多少RT

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(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)等于多少RT(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)等于多少RT(2^2+1)(2^4+1)

(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)等于多少RT
(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)等于多少
RT

(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)等于多少RT
思路:在原式乘上(2^2-1),不断的产生平方差,可以巧解.最后再除以3原式=(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1) /3 =(2^4-1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)/3 =(2^8-1)(2^8+1)(2^16+1)(2^32+1)/3 =(2^16-1)(2^16+1)(2^32+1)/3 =(2^32-1)(2^32+1)/3 =(2^64-1)/3