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Math Help - Proof by induction stuck on a sum help needed

  1. #1
    Member ssadi's Avatar
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    Proof by induction stuck on a sum help needed

    Code:
    Given that m is an odd positive integer, prove that 
    
    
    
    
    (m^2+3)(m^2+15) is divisible by 32 for all such values of m.
    I made it divisible by 8:
    ((k+2)^2+3)((k+2)^2+15)-((k^2+3)(k^2+15))<br />
  =8 (k^3+3k^2+13k+11)
    But I could not make it divisible by 32. A little help please, I feel I was very close to the solution.
    My method is right, right?
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  2. #2
    Moo
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    Hello,
    Quote Originally Posted by ssadi View Post
    Code:
    Given that m is an odd positive integer, prove that 
    
    
    
    
    (m^2+3)(m^2+15) is divisible by 32 for all such values of m.
    I made it divisible by 8:
    ((k+2)^2+3)((k+2)^2+15)-((k^2+3)(k^2+15))<br />
  =8 (k^3+3k^2+13k+11)
    But I could not make it divisible by 32. A little help please, I feel I was very close to the solution.
    My method is right, right?
    You can use the fact that k is odd, that is to say k=2n+1

    It'll give you what you want, but the method you use looks very long to me...
    Dunno if there's another way (thinking on it)
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