If $n>7$ is an integer, then $n=3m+5n$ where $m,n \in \mathbb{N}$. Basically all integers greater than or equal to $8$ can be written in the form
$$3m+5n.$$
Is there a generalized result where if $(a,b)=1$ and $a+b=k$ then can any integer greater than $k$ be written as a linear combo of $a,b??$