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Prove that it is divisible by 8.

  1. Aug 21, 2011 #1
    1. The problem statement, all variables and given/known data

    Prove 9n-1 is divisible by 8 such that n is positive integer.

    2. Relevant equations



    3. The attempt at a solution

    It looks simple and i tried to apply everything i know but yet i can't prove it. Any hints?
     
  2. jcsd
  3. Aug 21, 2011 #2

    dynamicsolo

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    Do you know modular (clock) arithmetic? What is 9 modulo 8? What about 92? What happens each time you multiply by another factor of 9?

    (If you aren't familiar with this device, think about a clock with "hours" from 0 to 7 [eight positions]. Start at "0" and count 9 "hours" forward; where do you end up? What happens for multiples of 9? Where is 92? What happens with higher powers of 9?

    Also, where are all multiples of 8 located on the clock?)
     
    Last edited: Aug 21, 2011
  4. Aug 21, 2011 #3

    uart

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    Science Advisor

    Hi Michael. It's very easy if you use induction.

    Consider how you could write [itex](9^{n+1} - 1)[/itex] in terms of [itex](9^n-1)[/itex].
     
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