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[Proof] Divisibility Proof

  1. Oct 22, 2012 #1
    1. The problem statement, all variables and given/known data

    Prove that for any n ∈ Z, n(n² − 1)(n + 2) is divisible by 12 .

    3. The attempt at a solution

    We first assume n = k for some value k.

    Next we assume k(k² − 1)(k + 2) = 12m for some value m.

    I don't know where to go from here. I don't think this is supposed to be an induction proof because our professor never explained induction to us yet. Every other proof i've seen for questions like this use induction (because it's so much easier to)...
     
    Last edited: Oct 22, 2012
  2. jcsd
  3. Oct 22, 2012 #2

    tiny-tim

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    hi twoski! :smile:

    (try using the X2 button just above the Reply box :wink:)

    hint: factor (n2 - 1) :wink:
     
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