Let $C, R \in \mathbb{Z}^n$. If there is an $n \times n$-matrix $M$ with all entries being integers such that the sum of the entries of column $k$ equals $C(k)$, and the sum of the entries of row $k$ equals $R(k)$, for all $k \in \{1,...,n\}$, we say that the pair $(C, R)$ is representable.
For $(C, R)$ to be representable, it is easy to see that we need $\sum_{i=1}^n C(i) = \sum_{i=1}^n R(i)$.
Does the converse hold?