(3-1)(3+1)(3²+1)······(3三十二次方+1)+2的个位数字
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(3-1)(3+1)(3²+1)······(3三十二次方+1)+2的个位数字
(3-1)(3+1)(3²+1)······(3三十二次方+1)+2的个位数字
(3-1)(3+1)(3²+1)······(3三十二次方+1)+2的个位数字
利用(a-b)(a+b)=a²-b²公式
原式=(3^2-1)(3^3+1).(3^32+1)+2=3^64-1+2=3^64+1
3^2→9,3^4→1,3^6→9,3^8→1,.
因此3^(2n),当n为奇数时余数为1;当n为偶数时余数为9
64/2=32
3^64→1
所以原式个位数字为2