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Math Help - prove that if n is divisible by 11 and n' is obtained from n by inserting two identic

  1. #1
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    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
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  2. #2
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    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.
    Thanks from virebbala90 and HallsofIvy
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