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Math Help - Contradiction proof

  1. #1
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    Contradiction proof

    Prove n is odd if and only if n^3 is odd. So we want to prove if n is odd then n^3 is not odd. Which is the contradiction.

    If n is odd then there exist a number in which n=2m+1. Where do I go from here to finish the proof?
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  2. #2
    Senior Member jakncoke's Avatar
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    ok, e n is odd and n^3 is even. By def of odd and even, there
     \exists \: m \in \mathbb{Z} such that  n = 2m + 1 similarly,  \exists \: k \in \mathbb{Z} such that  n^3 = 2k so  (2m+1)^3 = 2k if you remember what division meant, if a divides b then there exists an integer g such that b = ag. since k is an integer, this means 2 divides (2m+1)^3 which means 2 divides (2m+1) which is a contradiction.
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