Suppose $n_1$, $n_2$, $\dots$ $n_k$ are given natural numbers. Can we write the addition $\sum$ of these $k$ numbers in terms two other functions $f$ and $g$?
i.e. $\sum(n_1, n_2,\dots,n_k)=f(n_1, n_2,\dots,n_k)+g(n_1, n_2,\dots,n_k)$?
Clearly, the addition function needs $k-1$ steps to add the $k$ given natural numbers. But if we are able to get the functions $f$ and $g$ in such a manner that $f$ and $g$ can be evaluated for the $k$ numbers in one shot then addition of k number can be computed in two three steps.
Any help is highly solicited.