straightforward hcf question

Question

This shouldn't be difficult but I can't get it out..:

Let $c,d,N$ be integers with $\operatorname{hcf}(c,d,N) = 1$. Show that there exist $m, n ∈\mathbb Z$ with $\operatorname{hcf}(c+mN,d+nN) = 1$

Any help appreciated!