# prove that if n is divisible by 11 and n' is obtained from n by inserting two identic

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• October 1st 2013, 07:58 AM
virebbala90
prove that if n is divisible by 11 and n' is obtained from n by inserting two identic
prove that if n is divisible by 11 and n' is obtained from n by inserting two identical digits between consecutive digits of n, then n' is also divisible by 11. For example, since 407 is divisible by 11, the following are also divisible by 11: 22407, 43307, 40997 and 40722

please need elaborate and quick answer
• October 1st 2013, 07:59 PM
johng
Re: prove that if n is divisible by 11 and n' is obtained from n by inserting two ide
Hi,
Let $n=\sum_{i=0}^md_i10^i$. Use the fact that $10\equiv-1\,(\text{mod}\,\,11)$ and compute mod 11.