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Math Help - if n is even...

  1. #1
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    if n is even...

    for n \in \mathbb{Z} prove that n is even  \iff \ n -2 [\frac{n}{2}] =0
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by flower3 View Post
    for n \in \mathbb{Z} prove that n is even  \iff \ n -2 [\frac{n}{2}] =0
    Really? n=2z so that \frac{n}{2}=z so that \left\lfloor\frac{n}{2}\right\rfloor=z\implies2\le  ft\lfloor\frac{n}{2}\right\rfloor=2z=n
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  3. #3
    MHF Contributor chiph588@'s Avatar
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    The other way:

     n-2\lfloor \frac{n}{2} \rfloor = 0 \iff n=2\lfloor \frac{n}{2} \rfloor \implies 2\mid n \implies n is even.
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