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Divisibility of a prime

  1. Oct 3, 2009 #1
    if p is any prime other than 2 or 5, prove that p divides infinitely many of the integers 9, 99, 999, 9999, .... If p is any prime other than 2 or 5, prove that p divides infinitely many of the integers 1, 11, 111, 1111, ...

    Is there a way to do this problem using modular arithmetic? Thanks
     
  2. jcsd
  3. Oct 3, 2009 #2

    Hurkyl

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    Yes.
     
  4. Oct 3, 2009 #3
    I am stuck. Could you help me?
     
  5. Oct 3, 2009 #4

    Hurkyl

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    Where are you stuck? What have you done so far?
     
  6. Oct 3, 2009 #5
    On getting started.
     
  7. Oct 4, 2009 #6
    Can you prove that at least 2 different powers of 10 have to be equal to each other mod p?
     
    Last edited: Oct 4, 2009
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