Even number sum proof Prove that every even number $k\geqslant 8$ can be represented as $m,n\in \mathbb{N}\setminus \{1\}$
$$k=m+n$$
and $\gcd(m,n)=1$.
I was able to do it, if $k$ is an odd number but not if it is even. I could use some hints.

Hint: If $\mathrm{gcd}(k, m) = 1$, then if $q$ is an integer such that $q \mid m$ and $q \mid k-m$, then $$q \mid (k-m) + m = k$$
Can you deduce that $m$ and $k-m$ are coprime?
