作业帮计算3(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1的值要说明道理啊~!~~~~
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/03 09:12:14
计算3(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1的值要说明道理啊~!~~~~
计算3(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1的值
要说明道理啊~!~~~~
计算3(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1的值要说明道理啊~!~~~~
3(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1
=(2^4-1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1
=(2^8-1)(2^8+1)(2^16+1)(2^32+1)+1
=(2^16-1)(2^16+1)(2^32+1)+1
=(2^32-1)(2^32+1)+1
=2^64-1+1
=2^64
先把3写成(2^2-1),再连续用平方差公式
3(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1
=1*3*(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1
=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1
=(2^4-1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1
反复使用平方差
=2^64-1+1
=2^64
3=2^2-1;
3(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1=
(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1
=2^64-1+1
=2^64