Conjecture about divisibility: if $d \mid n$, then there exists $r,s$ such that $n=r+s$ and $d = \gcd(r,s)$

Question

Given $n\in\mathbb Z^+$. If $d<n>1$ and $d\mid n$ it exists $r,s\in \mathbb Z^+$ such that $n=r+s$ and $d=\gcd(r,s)$.

Answer 1

Let $r=d$ and $s=n-d$. It is easy to verify that their gcd is $d$.