for $\displaystyle n \in \mathbb{Z} $ prove that n is even $\displaystyle \iff \ n -2 [\frac{n}{2}] =0$

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- Feb 24th 2010, 11:49 PMflower3if n is even...
for $\displaystyle n \in \mathbb{Z} $ prove that n is even $\displaystyle \iff \ n -2 [\frac{n}{2}] =0$

- Feb 24th 2010, 11:58 PMDrexel28
- Feb 25th 2010, 08:30 PMchiph588@
The other way:

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