试确定(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1的末位数字
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试确定(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1的末位数字
![试确定(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1的末位数字](/uploads/image/z/4251057-33-7.jpg?t=%E8%AF%95%E7%A1%AE%E5%AE%9A%282%2B1%29%282%5E2%2B1%29%282%5E4%2B1%29%282%5E8%2B1%29%282%5E16%2B1%29%282%5E32%2B1%29%282%5E64%2B1%29%2B1%E7%9A%84%E6%9C%AB%E4%BD%8D%E6%95%B0%E5%AD%97)
2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1))(2^32+1)+1
=(2-1)(2+1)(2^2+1)...(2^32+1)(2^64+1)+1
=(2^2-1)(2^2+1)...(2^64+1)+1
=...
=(2^64-1)(2^64+1)+1
=2^128-1+1
=2^128
2^n的个位是以:2、4、8、6循环
128/4=32无余数
说明末位是6
=(2-1)(2+1)(2^2+1)...(2^32+1)(2^64+1)+1
=(2^2-1)(2^2+1)...(2^64+1)+1
=...
=(2^64-1)(2^64+1)+1
=2^128-1+1
=2^128
2^n的个位是以:2、4、8、6循环
128/4=32无余数
说明末位是6
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