# Prove that $\{ ax+by\mid x,y\in\mathbb Z\} = \{ n(a,b) \mid n\in\mathbb Z\}$ [duplicate]

Prove the following proposition:

Suppose $a,b$ are fixed integers. Then $\{ ax+by\mid x,y\in\mathbb Z\} = \{ n(a,b) \mid n\in\mathbb Z\}$.

• @robjohn It's an exact duplicate of the post I linked, even the same notation. I suggest merging. – user147263 Apr 4 '15 at 18:20