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Where do I start?

  1. Apr 7, 2005 #1
    Can someone point me in the right direction of solving the following problem:

    Prove that for any postive integer n, the value of the expression [tex]3^{2n+2} - 8n -9[/tex] is divisible by 64.
     
    Last edited: Apr 7, 2005
  2. jcsd
  3. Apr 7, 2005 #2

    honestrosewater

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    I find when you're asked to prove that every member of some subset of the natural numbers has some property, induction usually works.
     
  4. Apr 7, 2005 #3

    matt grime

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    9^{n+1}-8n-9

    or equivalently

    9^n-8n-1

    what is the binomial expansion of 9^n when considering 9=8+1?
     
  5. Apr 7, 2005 #4

    honestrosewater

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    Maybe I'm having a blonde moment, but doesn't [itex]a^{n + 1} - a = a(a^{n} - 1)[/itex], making [itex]9^{n + 1} - 9 - 8n = 9(9^{n} - 1) - 8n[/itex]?
     
  6. Apr 7, 2005 #5

    matt grime

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    ah, perhaps i ought to have been clearer: i wasn't say the epxressions are equal, but that if you prove one is divisible by 64 for all n, the other will be divislbe by 64 for all n (give or take a case when n=0). I let m=n+1 in the first, then relabelled n=m.
     
  7. Apr 9, 2005 #6
    I get it now. Thank you.
     
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