3^1=3,3^=9,3^3=27.3^8=6561

来源:学生作业帮助网 编辑:作业帮 时间:2024/12/01 09:51:21
3^1=3,3^=9,3^3=27.3^8=6561
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3^1=3,3^=9,3^3=27.3^8=6561
3^1=3,3^=9,3^3=27.3^8=6561

3^1=3,3^=9,3^3=27.3^8=6561
反复运用平方差公式:
(3-1)(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)+2
=(3^2-1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)+2
=(3^4-1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)+2
=(3^8-1)(3^8+1)(3^16+1)(3^32+1)+2
=(3^16-1)(3^16+1)(3^32+1)+2
=(3^32-1)(3^32+1)+2
=(3^64-1)+2
=3^64+1
注意到3的幂的个位数是按照3、9、7、1依次循环的,故3^64的个位数与3^4的个位数相同是1
因此所求个位数是3