1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Direct Proof Integers Date
Proof regarding direct sum of the dual space of a v-space Jan 19, 2017
Direct proofs Nov 27, 2016
Direct Sum: Vector Spaces Feb 29, 2016
Discrete Math Question Nov 12, 2014
Direct proof confusion? Sep 6, 2012