# Math Help - if n is even...

1. ## if n is even...

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

2. Originally Posted by flower3
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 $\left\lfloor\frac{n}{2}\right\rfloor=z\implies2\le ft\lfloor\frac{n}{2}\right\rfloor=2z=n$

3. 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.