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Homework Help: If x is odd, then 2^x + 3^x is also odd

  1. Apr 12, 2010 #1
    1. The problem statement, all variables and given/known data

    Prove: If x is a positive odd integer, then [tex]2^x + 3^x[/tex] is also a positive odd integer.

    3. The attempt at a solution

    Assume x is odd; there exists an integer k such that x = 2k + 1. Then
    [tex]2^x + 3^x = 2^{2k+1} + 3^{2k+1}[/tex]

    I don't know how to go about simplifying it from here.
  2. jcsd
  3. Apr 12, 2010 #2


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    Re: Proof

    Is 2^x even or odd? What about 3^x? I'm a bit confused why they are specifying x odd. Isn't it true even if x is even?
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