Here it is:
$c , n \in \mathbb{N}$ and $x_1,x_2,\ldots,x_n \in \mathbb{N}\cup \{0\}$
$c= 1 x_1 + 2 x_2 + \ldots + n x_n$
How many solutions $\{x_1,x_2,\ldots,x_n\}$ are there?
I do not know number theory. However, i think that what I am looking at is a number theory problem. It is a counting problem that arises from a statistical physics toy model i am working on.
The solution may be trivial and in textbooks or it could be a hard problem. I don't know that is why i am asking, for guidance on what kind of set of skills deals with these things. Thanks anyone. mario