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来源:百度文库 编辑:高校问答 时间:2024/04/27 15:39:34
用平方差公式计算:2*(3+1)*(3^2+1)(3^4+1)(3^8+1)...(3^32+1)+1

2*(3+1)*(3^2+1)(3^4+1)(3^8+1)...(3^32+1)+1
=2*[1/(3-1)]*(3-1)*(3+1)*(3^2+1)(3^4+1)(3^8+1)... (3^32+1)+1
=2*[1/(3-1)]*(3^2-1))*(3^2+1)(3^4+1)(3^8+1)... (3^32+1)+1
=2*[1/(3-1)]*(3^4-1)(3^4+1)(3^8+1)... (3^32+1)+1
=2*[1/(3-1)]*(3^8-1)(3^4+1)(3^8+1)... (3^32+1)+1
………………………………………………
=2*[1/(3-1)]*(3^32-1)(3^32+1)+1
=2*[1/(3-1)]*(3^64-1)+1
=3^64

2=3-1
原式=(3-1)(3+1)(3^2+1).......(3^32+1)+1
=(3^2-1)(3^2+1).......(3^32+1)+1
=(3^32-1)*(3^32+1)+1
=3^64-1+1
=3^64

2*(3+1)*(3^2+1)(3^4+1)(3^8+1)...(3^32+1)+1
=(3-1)*(3+1)*(3^2+1)(3^4+1)(3^8+1)...(3^32+1)+1
=(3^2-1)*(3^2+1)(3^4+1)(3^8+1)...(3^32+1)+1
=(3^4-1)(3^4+1)(3^8+1)...(3^32+1)+1
=(3^8-1)(3^8+1)...(3^32+1)+1
=(3^16-1)(3^16+1)(3^32+1)+1
=(3^32-1)(3^32+1)+1
=3^64-1+1
=3^64

2*(3+1)*(3^2+1)(3^4+1)(3^8+1)...(3^32+1)+1
=2*(3+1)*(3^2+1)(3^4+1)(3^8+1)...(3^32+1)*(3-1)/2+1
=(3-1)*(3+1)*(3^2+1)(3^4+1)(3^8+1)...(3^32+1)+1
=(3^2-1)(3^4+1)(3^8+1)...(3^32+1)+1
=3^64+2

2*(3+1)*(3^2+1)(3^4+1)(3^8+1)...(3^32+1)*(3-1)/2+1
=(3^2-1)*(3^2+1)(3^4+1)(3^8+1)...(3^32+1)
=(3^32-1)(3^32+1)
=(3^64+1)