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Direct Proof With Odd Integers

  1. Nov 16, 2007 #1
    1. The problem statement, all variables and given/known data
    If m is an odd integer and n divides m, then n is an odd integer.


    2. Relevant equations
    Odd integers can be written in the form m=2k+1.
    Since n divides m, there exists an integer p such that m=np


    3. The attempt at a solution
    We will assume that m is an odd integer and that n divides m. We will show that n is an odd integer. Since m is an odd integer, there exists an integer k such that m=2k+1. Since n divides m, there exists an integer p such that m=np.

    I don't know where to go from here to arrive at n is equal to 2*an integer +1. Do I need to use cases?
     
  2. jcsd
  3. Nov 16, 2007 #2
    so you have m = np and m is odd. you want to show n is odd. so suppose it's even, then look what happens, you should get a contradiction.
     
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