  The article presents the existence and mass conservation of solution for the
discrete Safronov-Dubovski coagulation equation for the product coalescence
coefficients $\phi$ such that $\phi_{i,j} \leq ij$ $\forall$ $i,j \in
\mathbb{N}$. Both conservative and non-conservative truncated systems are used
to analyse the infinite system of ODEs. In the conservative case, Helly's
selection theorem is used to prove the global existence while for the
non-conservative part, we make use of the refined version of De la
Vall\'ee-Poussin theorem to establish the existence. Further, it is shown that
these solutions conserve density. Finally, the solutions are shown to be unique
when the kernel $\phi_{i,j} \leq \text{min}\{i^\eta,j^{\eta}\}$ where $\eta \in
[0,2]$.
