Given integers $a_1, \ldots, a_n, b \in \mathbb{N}$. What is the complexity of the following problem$$ \exists x_1, \ldots, x_n \in \mathbb{N} \text{ such that } a_1x_1 + \ldots a_nx_n = b? $$I can't find this subset-sum variant in the literature.
Complexity of a subset sum variant
cc.complexity theory;np hardness;subset sum