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Induction! physics question

  1. Nov 5, 2009 #1
    1. The problem statement, all variables and given/known data

    prove that for all n>0 , 4^n + 15n - 1 is divisible by 9/multiple of 9


    2. Relevant equations




    3. The attempt at a solution
    need to show: 4^(n+1) + 15(n+1) + 14/9 = a*k a and k are integers
    assumption to inductive step: (4^n + 15n - 1)/9 = k --> 4^n + 15n - 1 = 9k -->
    4^n+1 + 60n - 4 = 36k.. now what? I tried 4^n+1 -4 = 6(6k - 10n) but ultimately , I am stuck

    please help! tank you
     
    Last edited: Nov 5, 2009
  2. jcsd
  3. Nov 5, 2009 #2

    Avodyne

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    Science Advisor

    Re: induction!

    Where did you get this?

    Let f(n) = 4^n + 15n - 1. First, you need to show that f(1) is divisible by 9. Then, you need to show that f(n+1) is divisible by 9 if f(n) is.
     
  4. Nov 5, 2009 #3
    Re: induction!

    sorry , I had a typo. thanks for the reply but I got the answer!
     
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