IMO Shortlist 1989 problem 19

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Dodao/la: arhiva
2. travnja 2012.
A natural number is written in each square of an m \times n chess board. The allowed move is to add an integer k to each of two adjacent numbers in such a way that non-negative numbers are obtained. (Two squares are adjacent if they have a common side.) Find a necessary and sufficient condition for it to be possible for all the numbers to be zero after finitely many operations.
Izvor: Međunarodna matematička olimpijada, shortlist 1989