A FUNCTION F IS CALLED GOOD IF IT ASSIGNS AN INTEGER VALUE F (M, N)...

6. 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:

2 f (m, n) = f (m − n , n − m) + m + n = f (m + 1 , n) + f (m, n + 1) − 1.

Find all good functions.

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