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A hundred one digits number is formed by writing natural numbers (starting from 1) as 12345678910111213…. Find the remainder when this number is divided by




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Since 8\mid 10^3, it is sufficient to check the last 3 digits.

1-9 : 9 digits
10-55 : 46*2 = 92 digits

That means the number ends with \ldots 53545 and the last 3 digits are 545 :
0 0 0
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