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The question is , if f(n)= 1+10+10^2 + + 10^n , where n is

  1. Dec 5, 2012 #1
    the question is , if f(n)= 1+10+10^2 +... + 10^n , where n is integer.
    find the least n s.t. f(n) is divisible by 17 , I have no idea about it.
     
  2. jcsd
  3. Dec 5, 2012 #2

    mfb

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    Re: divisible

    What is the remainder if you divide...
    1 by 17?
    10 by 17?
    100 by 17?
    ...
    a+b by 17, if you know it for a and b?

    That should help.
     
  4. Dec 5, 2012 #3
    Re: divisible

    It should also help to recognize that 9 times the sum plus 1 is a power of 10. Thus Fermats Little theorem re primes P dividing A^(P-1) - 1 may apply.
     
  5. Dec 5, 2012 #4
    Re: divisible

    You can also find n by "brute force", i.e. check if f(1), f(2), f(3), ... is divisible by 17. Use http://www.wolframalpha.com/ or write a small program in your programming language of choice.
     
    Last edited: Dec 5, 2012
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