若甲=6666....6, 共一百位數, 求甲除9的餘數?

1. 若甲=6666....6, 共一百位數，求甲除9的餘數?
Sol
6*100/9=66……..6
餘數=6

2. 9999999999*5555555555之積的各個數字總和是多少?
Sol
9999999999*5555555555
=(10000000000－1)*5555555555
=55555555550000000000－5555555555
=55555555544444444445
5*(9+1)+4*10
=90
or
9*5=45
4+5=9
a1=9
99*55=5445
5*2+4*2=18
a2=18
a3=999*555=554445
5*3+4*3=27
a3=27
9999*5555=55544445
5*4+4*4=36
a4=36
成等差a1=9，d=9
a10=a1+9d=9+9*8=90

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9999999999*5555555555
=(10000000000-1)*5555555555
=55555555550000000000 - 5555555555
=55555555544444444445
總和=5*10+4*10 = 90

(1)

Sol
666(mod9)=0
So
(666*10^97+666*10^94+666*10^1+6) (mod9)=6

(2):

9*1111111111*5*1111111111
=45*(1111111111)^2

Sol
5+4+(5+4)*(10-1) = 90.

9x5=54??

這個......= =