, 2020

A function $f$ is called good if it assigns an integer value $f(m, n)$ to every ordered pair of integers $(m, n)$ in such a way that for every pair of integers $(m, n)$ we have:
$$2f(m, n) = f(m - n, n - m) + m + n = f(m + 1, n) + f(m, n + 1) - 1.$$
Find all good functions.