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Mathematical Induction

  1. May 5, 2015 #1
    1. The problem statement, all variables and given/known data
    Prove that (n2+3)(n2+15) is divisible by 32 for all odd positive integers n.

    2. Relevant equations
    I suppose we are supposed to use mathematical induction since it is in that chapter, but the following questions specifically state that we should use induction but this question doesn't.

    3. The attempt at a solution
    n=1
    (1+3)(1+15)=64=2*32​
    n=k
    (k2+3)(k2+15)=32A, A∈ℝ​
    n=k+1
    ⇒((k+2)2+3)((k+2)2+15)
    = (k2+3)(k2+15) + 8k3+24k2+104k+88
    = 32A + 8(k3+3k2+13k+11)​
     
  2. jcsd
  3. May 5, 2015 #2

    haruspex

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    You don't mean that.
    Think about that choice again. Note that it says:
     
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