by monalisa
Last Updated April 15, 2019 11:20 AM

I considered an even number $n\geq 9$, where it is divisible by some positive integer $k$.

Also, $k$ does not divide $\frac{n}{2}$.

Let $n = kq$.

Can we say that $q$ is even in this case? Can anyone help to get it theoretically? Thanks a lot for the help.

**My attempt:**

Let $n = kq$.

Since $k$ does not divide $\frac{n}{2}$, we have

$n/2 = k.q_1 + r$ for $0<r\leq k-1$.

How to conclude the even or odd property of $k$ and $q$ here?

As a counter example, take $n = 14$ and $k = 2$. Then $2$ does not divide $14/2 = 7$ and $q = 7$ is not an even number.

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