求1的2012次幂+2的2012次幂+···+9的2012次幂的末位数字

求1的2012次幂+2的2012次幂+···+9的2012次幂的末位数字
求1的2012次幂+2的2012次幂+···+9的2012次幂的末位数字

求1的2012次幂+2的2012次幂+···+9的2012次幂的末位数字
49

mod(1^n,10) = 1, mod(1²º¹², 10) = 1
mod(2⁴ⁿ,10) = 6, mod(2⁴ⁿ+¹,10) = 2, mod(2⁴ⁿ+²,10) = 4, mod(2⁴ⁿ+³,10) = 8, mod...

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mod(1^n,10) = 1, mod(1²º¹², 10) = 1
mod(2⁴ⁿ,10) = 6, mod(2⁴ⁿ+¹,10) = 2, mod(2⁴ⁿ+²,10) = 4, mod(2⁴ⁿ+³,10) = 8, mod(2²º¹²,10) = 6
mod(3⁴ⁿ,10) = 1, mod(3⁴ⁿ+¹,10) = 3, mod(3⁴ⁿ+²,10) = 9, mod(3⁴ⁿ+³,10) = 7, mod(3²º¹²,10) = 1
mod(4²ⁿ,10) = 6, mod(4²ⁿ+¹,10) = 4, mod(4²º¹²,10) = 6
mod(5ⁿ,10) = 5, mod(5²º¹²,10) = 5
mod(6ⁿ,10) = 6, mod(6²º¹²,10) = 6
mod(7⁴ⁿ,10) = 1, mod(7⁴ⁿ+¹,10) = 7, mod(7⁴ⁿ+²,10) = 9, mod(7⁴ⁿ+³,10) = 3, mod(7²º¹²,10) = 1
mod(8⁴ⁿ,10) = 6, mod(8⁴ⁿ+¹,10) = 8, mod(8⁴ⁿ+²,10) = 4, mod(8⁴ⁿ+³,10) = 2, mod(8²º¹²,10) = 6
mod(9²ⁿ,10) = 1, mod(9²ⁿ+¹,10) = 9, mod(9²º¹²,10) = 1
mod(1²º¹² + 2²º¹² +... + 9²º¹² , 10) = mod(1 + 6 + 1 + 6 + 5 + 6 + 1 + 6 + 1 , 10) = 3

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答案为3。
詹佳晴写错了。。。。