Necessary and sufficient condition for a linear diophantine equation to have natural solution

Question

Is there any necessary and sufficient condition for the linear diophantine equation $$\sum_{i = 1}^{n}a_{i}x_{i} = c$$ to have a natural solution (at least when $n = 3$), where $a_{i}$s and $c$ are integers and $n$ is natural and at least one of $a_{i}$s is nonzero?