1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    Homework Helper

    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


    User Avatar
    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].
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook