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~!~~~~
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![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~!~~~~](/uploads/image/z/116393-41-3.jpg?t=%E8%AE%A1%E7%AE%973%282%5E2%2B1%29%282%5E4%2B1%29%282%5E8%2B1%29%282%5E16%2B1%29%282%5E32%2B1%29%2B1%E7%9A%84%E5%80%BC%E8%A6%81%E8%AF%B4%E6%98%8E%E9%81%93%E7%90%86%E5%95%8A%7E%21%7E%7E%7E%7E)
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