求2(3+1)(3^2+1)(3^4+1)L(3^256)+1的个位数字

2024-12-14 01:36:35
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回答1:

2(3+1)(3^2+1)(3^4+1)……(3^256+1)

=(3-1)(3+1)(3²+1)(3^4+1)……(3^256+1)
=(3²-1)(3²+1)(3^4+1)……(3^256+1)
=(3^4-1)(3^4+1)……(3^256+1)
=(3^256-1)(3^256+1)
=3^512-1
3^4k末位为1
3^4k+1末位为3
3^4k+2末位为9
3^4k+3末位为7
3^512-1末位为0