I understand the theory of how to prove a mutli variable function bijective, however I somehow can neither prove this function injective or surjective:
$$f: \mathbb N\times \mathbb N \rightarrow \mathbb N, (a, b) \mapsto {(a+b)}^{2} + a$$
I tried to start with $f(a, b) = f(a', b')$ but I don't really know how to continue from there. To prove it surjective I started with: show that for every $n$ there is $(a, b)$ with $f(a, b) = m$ but was not successful there either. To make matters worse I don't even know yet if this function is injective, surjective, neither or both. Any help would be appreciated!