计算3(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1的末位数字

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/27 14:40:36
计算3(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1的末位数字

计算3(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1的末位数字
计算3(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1的末位数字

计算3(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1的末位数字
(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)/(2^2-1)
=(2^4-1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)/(2^2-1)
=(2^8-1)(2^8+1)(2^16+1)(2^32+1)/(2^2-1)
……
=(2^64-1)/3
原式=(2^64-1)+1=2^64
2^1=2
2^2=4
2^3=8
2^4=16
2^5=32
2^6=64……
尾数2,4,8,6四个一循环
2^64中64是4的倍数,尾数是6