Question

8(9+1)(9平方+1)(9的4次方+1)(9的8次方+1)+1的个位数字

Answer 1

8(9+1)(9^2+1)(9^4+1)(9^8+1)+1

=(9-1)(9+1)(9^2+1)(9^4+1)(9^8+1)+1

=(9^2-1)(9^2+1)(9^4+1)(9^8+1)+1

=(9^4-1)(9^4+1)(9^8+1)+1

=(9^8-1)(9^8+1)+1

=9^16-1+1

=9^16

=81^8

因为81整数次方的个位数字都是1,

所以8(9+1)(9平方+1)(9的4次方+1)(9的8次方+1)+1的个位数字是1